What Type of Plastic are Door Armrest Bases?
I mean this as an addition to OldManMoPar's excellent advice, and not to imply that there is anything wrong with it, as he clearly knows what he is talking about, but I was just working on my original '64 armrest base, which had one hole ripped out of it.
First, it definitely feels like polystyrene, but I am not any kind of expert.
Second, it definitely softens with lacquer thinner like polystyrene.
Third, depending on what you are actually fixing, and how much is visible (the inside of your armrest base will never be seen again by human eyes), you may want to make a visual repair as he recommends above, and then make a structural repair on the back side, using epoxy putty, with or without embedded wire or window screen, to be sure it holds.
In my own case, I used those dumb "wood repair" plates, about 1/6" thick, cut and drilled to size, to act as sort of giant washers to distribute the screws' clamping force across the plastic shelf, epoxied them in place with viscous epoxy, then reinforced the webbing with epoxy putty, hopefully providing enough strength to slam the door shut against the nice, new, stiff weatherstipping.
Good luck!
- Eric