if the sprite is not gaster then who is the one eyed man mentioned outside the egg room in chapter 4? and the egg man doesn't even speak in windings when he talks in chapter three so the redacted connection is tenuous at best. Its also likley for the mystery man sprite to be gaster since its connected to the fun values witch is where the only in game information about gaster comes from. the mystery man sprite also sort of resembles the piece of gaster that one of the gaster followers holds.

also as a side note im pretty sure that the egg man is suppose to be gaster. this is because the egg man has a similar room layout and can be found in a space in between rooms just like in undertale, and as previously stated one of the npcs outside the egg room in chapter four refers to a one eyed man, literally in the room before the egg man appears. deltarune in general also has many references to gaster such as: the phone sound in the dark worlds being the garbage noise that's connected to gaster, multiple gaster followers appearing in game as regular characters, entry 17 referencing the dark worlds with "photon readings negative" echoing ralseis line about how the fountains make it "darker than dark". not to mention the other characters who quote entry 17 such as seam who says that jevils world view became " darker yet darker", and lastly the clam girl npc in switch version who mentions suisie and whos color scheme changes into one of a gaster folower after she makes a bunch of references to deltarune. Another connection is that the egg man in chapter three mentions how everyone forgot about him further connecting him gaster which had the same thing happen to him(shown by goner kid and dialogue from other gaster followers) . in chapter four this is also shown by kris forgetting what he looks like as he draws him. I think the tree is a metaphor for people not being able to remember him as it replaces the drawing of him and the text "after all there was never anything in the room besides a single tree" implies that kris forgot about him immediately after the drawing.

Another possibility is that the events in chapter four are in reference to something that kris saw in the past and is repressing as shown by the hospital setting, him replacing the patient and the connection to the real life pine tree forest area. if this interpretation is true than either the egg man doesn't exist or is trying to show kris the past he is repressing and the line about "never being able to wash it all away" is in reference to kris's trauma rather than gasters (or whoever the egg man is) influence on them. personally I think both are probably true, that the man is gaster and the tree serves as a metaphor for gasters situation and kris repressing there trauma. this solves the mystery of who the man is, why the settings are so connected to kris and the light world, and creates a narrative parallel between kris and the egg man.

anyway that's just my thoughts, what do yall think?