Okay so you know you're getting power and ground to it, to have up/down work.
I'd take it (whole seat) out, flipped on its side or upside down and power it from whatever, even brief use from an 18V cordless tool battery won't be enough to harm it for a test. I'd measure for voltage to, and whether it comes out of the forwards/reverse switch and makes it to the motor.
I'd check whether the mechanism seems to be binding and lube it. You could also remove the motor and see if it spins freely, directly applying power to it.
If it turns out to be the switch, then "maybe" (unless the plastic cracked), it can be opened and the contacts cleaned, or if broken internally then at least you can declare it dead. If it's the switch then I'd be tempted to get one from a junkyard, but having recently sorted through thousands of switches for a stove, I found there are all kinds of possibilities if it's a standard form factor, especially if you can make a mounting bracket for it, for example out of ~2mm thick sheet aluminum. I may be making this more complicated than it is.
Motor, if it won't spin with direct power to it, there's probably metal tabs needing bent or welds drilled out to open it. Might just need new brushes, but you can ohm out the windings with a multimeter and check for a blown thermal fuse inside. It'd be a good idea to lube that too if/when it's open.
See attached wiring