I thought this might be a good idea since I visit Pick-a-Part and other junkyards like that pretty frequently. It could be helpful for some looking for interiors and maybe engines, but a vast majority of Supras I find are MK2's and MK3's (I don't think a MK4 would ever end up around here).
I found two MkIII's in Pick-a-Part Monrovia: a white '86.5 with '89 three piece wing (center piece doesn't have the brake light), shadow grey interior, 7m-ge, and W58 tranny is gone.
Also found a red '89 Supra, shadow grey interior, 7m-ge, auto tranny, and 3 piece wing was taken except for the center part thrown in the trunk.
Also quite a few MK2's here also but I'm not sure what to keep a lookout for on them.
They have a 50% off thing going right now that ends Jan 1st at all the pick-a-part locations. I hope this is helpful to you guys cuz I know I would like a sneak peek at junkyards before I go!