Try cleaning the buttons? The inside of the buttons get a fair amount of wear and tear and tend to gum up. They simply snap apart (be careful, there are two tiny ball bearings inside). If you look at the contacts, most likely they are covered in black stuff from old age which you can clean off with some Q-tips and rubbing alcohol. Reassemble and put the switches back in to try them. I also think that the front switches must be operational or at least hooked up to allow power to go to the back windows.

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87 300E
202k on the clock