In 1918, in Aviles, Spain, several people woke up without their eyes. Though blinded, they were unharmed. The victims all described seeing a cloaked man holding an hourglass who threw sand in their eyes before they woke up. 
When two teams of Ghostbusters captured Proteus in their Proton Streams, the god was forced to show them the future. Since eight men captured him at once, he had to show eight futures at once. One of the futures gleaned was of the Sandman in silhouette. About one week later, the Sandman aided Karen Pearson in falling asleep the night before a big trip and took her right eye. The next morning, the police were called. Brent Mitchell from the 120th precinct went to the Ghostbusters for their help. The Ghostbusters entered the Pearson home on Staten Island and initially picked up no P.K.E. readings. The Sandman suddenly manifested in the middle of the living room. Ray Stantz noticed he was doing something with his hourglass but Peter Venkman opened fire. The Ghostbusters were unknowingly forced into a dream state. Sandman planned to spare Winston Zeddemore, Peter, and Ray. They believed Peter blew up the Sandman with his Proton Stream and blue Ectoplasm splashed all over them. Ray was the first to realize they were dreaming thanks to a visit from his spirit guide. The spirit guide was unable to directly intervene but could reconnect Ray with the others. He instructed Ray to snap them out of their delusion and they could take a little control of their current circumstances. The spirit guide shoved Ray through a mirror.
Ray reunited with Peter then Winston and Egon Spengler. Just as Egon remarked it was good they were reunited, the Ghostbusters were surrounded by giant eyes. Egon directed the others to attack by visualizing a memory of their equipment. He imagined the Boson Pack and opened fire on one of the eyes. The others followed suit and the Sandman experienced pain. The eye shape shifted into the Sandman's true form. He erected a barrier between Egon and the others. The Sandman manifested from the barrier and grabbed Egon. He admitted no one ever fought him before nor caused him pain.  He brandished a curved blade and began carving one of Egon's eyes out and promised it would be much better when he was done because Egon would only see darkness and thus, be able to sleep. Ray, Peter, and Winston destroyed his barrier in time. Egon quickly told them to fire on the Sandman's hourglass totem. He was forcibly dispersed and the Ghostbusters were released from his influence. They fell to the floor of the Pearson home.
Based on Mythology
Like Sinterklaas and Santa Claus, there's more than one layer to the Sandman legend. Many stories like Hans Christian Anderson's Ole Lukoje offer an alternative and sanitized take on the entity as a benevolent spirit that wanted children to sleep so he could tells stories. Ernst Hoffman wrote about a more sinister version who threw sand into the eyes of children that resisted sleep and then took their eyes to feed his own children, who lived on the Moon.
The Sandman removes eyes from his target while he or she is in a lucid dream state where their base consciousness is hijacked.  It is similar to a forced trip to the collective subconscious caused by the Draugar.  A telltale sign of being such a state is an ivory doorway.  The Sandman has control over the environment and can shift its appearance and raise constructs such as walls. He can also teleport at will, shapeshift his form, and reduce constructs created by his victim into sand. When the victim awakens, the eye is also removed but no optic nerves are severed.  If the Sandman's hourglass totem is destroyed in the dream state, he is dispersed and the victim(s) are released from his hold but any physical damage he inflicted in the dream state is preserved.
The Ecto Goggles registered a reading, of the Sandman, of 1989 MHz and an EMF of 10 to the tenth power.
Tobin's Spirit Guide
In Tobin's Spirit Guide, an entry about the Sandman begins with "A nursery monster from the 19th century used to scare children. During the early part of the century the Sandman brought terror among children as it would sneak into the rooms of young ones who would not go to sleep. The Sandman would throw sand into the eyes of children causing them to itch. When the child rubbed its eyes, his or her eyes would fall out on the floor creating a bloody mess. The Sandman would collect these..." and an drawing of the entity is accompanied by some Latin. "Somnum sempiternum" loosely translates to "sleep eternally" and "oculus satietas" which loosely translates to "sight satiation."
- Erik Burnham hinted the "voice" he picked for the character "dovetailed together eerily well."  The Sandman is definitely based on someone specific. 
- Sandman was meant to be read with Phil Hartman's oiliest voice. 
- The Moon in the background of the Ghostbusters Annual 2015 Regular Cover is a nod to E.T.A. Hoffman's "Der Sandman" as the Sandman was said to take his eyes to his iron nest on the Moon.
- On page 27 of Annual 2015:
- Peter mentions "Dream Me a Dream," in reference to the "Mr. Sandman" 1954 song performed by the Chordettes.
- On the Tobin page with just writing is a partial quote of the Sandman entry on the mythicalcreatureslist.com Sandman page
- The full article reads as "A nursery monster from the 19th century used to scare children. During the early part of the century the Sandman brought terror among children as it would sneak into the rooms of young ones who would not go to sleep. The Sandman would throw sand into the eyes of children causing them to itch. When the child rubbed its eyes, his or her eyes would fall out on the floor creating a bloody mess. The Sandman would collect these eyes to feed to his pet bird creature that lived on the crest of a moon. By the late 19th century, the Sandman had transformed into a benign character that brought children pleasant and happy dreams. This led to confusion about the Sandman as some believed that there were two Sandmen, one who had good intentions and another, a counterpart who had evil intentions. This friendly mythical creature gave one the power to choose what they would like to dream about and sometimes the Sandman granted a dream which revealed the sleeper's future. It is said that the grit or 'sleep' (scientifically known as rheum) in one's eyes upon waking is supposed to be the result of the Sandman's work the previous evening." 
- The rogue Sandman from The Real Ghostbusters episode "Mr. Sandman, Dream Me a Dream" appears on the right page of Tobin's Spirit Guide.
- Ray mentions Hans Christian Anderson and his story about Ole Lukoje, a more benevolent Sandman.
- On page 28 Annual 2015, Ray mentions Ernst Hoffman, who wrote "Der Sandmann" - a book published in 1917 from which this Sandman is based on.
- In Ghostbusters Annual 2017, on page 39, in panel 2, on the shelf left of Kylie's left leg is the Sandman's hourglass.
- On page 16 of Ghostbusters Crossing Over Issue #2, one of the images conjured is of Sandman.
- IDW Comics
- Insight Editions
- Ray Stantz (2015). IDW Comics- "Ghostbusters Annual 2015" (2015) (Comic p.27). Ray Stantz says: "Unsurprisingly, he's called the Sandman."
- What Came Before! (2016). IDW Comics- "Ghostbusters International #1" (2016) (Comic What Came Before!). Line reads: "The Sandman is a predatory spirit that manifests in the subconscious... and while the Ghostbusters were able to defend themselves and disperse the entity, since they faced it on the mental plane, they were unable to trap it."
- Narrator (2016). Insight Editions- "Tobin's Spirit Guide" (2016) (Book p.41). Paragraph reads: "In 1918, in Aviles, Spain, there were stories of people waking up without their eyes."
- Sandman (2015). IDW Comics- "Ghostbusters Annual 2015" (2015) (Comic p.22). Sandman says: "You know, no one has ever fought me before, let alone caused me pain. You're all very special."
- Narrator (2016). Insight Editions- "Tobin's Spirit Guide" (2016) (Book p.41). Paragraph reads: "CLASS VII."
- Ray Stantz (2015). IDW Comics- "Ghostbusters Annual 2015" (2015) (Comic p.16). Ray Stantz says: "We're in, like, a dream reality! A hijacking of our base consciousness!"
- Egon Spengler (2015). IDW Comics- "Ghostbusters Annual 2015" (2015) (Comic p.19). Egon Spengler says: "I've experienced a forced trip to the collective subconscious before, if you'll recall this feels almost exactly the same."
- Ray Stantz (2015). IDW Comics- "Ghostbusters Annual 2015" (2015) (Comic p.27). Ray Stantz says: "It was the ivory on the door frame that stood out. Y'know, like with the Greek Oneroi -- How they used an ivory gate to send dreams that were full of lies?"
- Brent Mitchell (2015). IDW Comics- "Ghostbusters Annual 2015" (2015) (Comic p.5). Brent Mitchell says: "The nerves aren't severed, Dr. Venkman. Her eye wasn't cut out. It's plain gone."
- erikburnham Tweet #1 8/14/15
- Erik Burnham Fan Page reply 7/23/15
- erikburnham Tweet 3/8/18
- mythicalcreatureslist.com Sandman page
- What Came Before! (2016). IDW Comics- "Ghostbusters International #1" (2016) (Comic What Came Before!). Line reads: "While the ladies were fending off a mountain of paperwork in the land of the rising sun, the Ghostbusters were called in to Staten Island, where they faced an entity called the Sandman (As seen in the GHOSTBUSTERS ANNUAL 2015)."
- What Came Before Page (2017). IDW Comics- "Ghostbusters 101 #1" (2017) (Comic What Came Before Page). Narrator says: "Demons that can attack the sleeping mind!"
- Narrator (2016). Insight Editions- "Tobin's Spirit Guide" (2016) (Book p.22). Paragraph reads: "They should not be confused with those entities that enter the subconscious mind of a sleeping individual, usually to do harm (for more on nocturnal entities, see the entry on the Sandman on page 41)."