As shown in the first and second game, tints and turps are entities derived from paint and thinner respectively. However, Gilda's white guardian appears to be neither a tint nor a turp. However, in the second game, the caverns reveal a few important alternatives.
Neutral pools are a translucent white. Also, if paint and thinner refills overlap, the glow appears white. Maybe this guardian is a middle ground?
The wells poured both invisible and indelible/invincible ink, the former of which is a clear white. Perhaps there could be guardians created by ink.
When the angel statues are pushed off of the angel caverns, white/purple ghosts circle around it's former position.
Maybe it was a spirit of sketches, as she spent a good period of time hiding in Mickeyjunk Mountain, a place swarming with loose sketches and items related to them.
My favorite theory: The Spirit of Wasteland embodies the important traits that make up the community of citizens in Wasteland. Maybe her guardian is an embodiment of Ortensia, the Spirit of Tomorrow. My belief is that after Ortensia was turned to inert by the blot, her spirit lingered in Mickeyjunk Mountain, until she came across the hiding Gilda, and began to follow her. Both Gilda and Ortensia have a certain spiritual link, given that Gilda is the Spirit of Heritage (the past) and The Spirit of Tomorrow (future). It is interesting to note that Gilda seemed to show up in hub locations when Mickey returned, and would always have races for him. It is proven that Oswald is a great racer, as he completed Ace's three projector challenge in half of Mickey's time. Maybe Ortensia hoped to catch Oswald's attention with the races, which she never did. In the second game, Gilda no longer has her guardian. When the bloticles attack, Gilda decides to go to an unknown location afterwards, which may have been to help destroy the blot and/or protect the citizens.
As a side note, the Sprite may also be a guardian that embodies a spirit of wasteland. In this case, it is Colonel Pete, the Spirit of Adventure. My theory is that Colonel Pete was one of the leaders in the fight for Wasteland during the Blot Wars. It's likely that he made a last stand trying to protect Lonesome Manor, and left his film reel as a legacy inside the manor before he and his forces were killed by The Mad Doctor and his Beetleworks. That could explain why different renditions of Pete appear in all major parts of Wasteland except Lonesome Manor (and Mickeyjunk Mountain, as it is occupied by Oswald). Much like Ortensia following Gilda, Colonel Pete follows Pete Pan as he goes on adventures, giving him courage while they are together.