Looks like a RocTec drive. Those are a pain to get working at this age. I have one that is intermittent. A disk cleaning kit helped a little but it seems to be pesky on some disks. I found that having it read a bunch of disks has helped get it "awake" and working again. I also read that these drives have a tendency to have the drive belt break. Some chaps over in the UK have got replacement belts and got it working again. (saw the thread over on English Amiga Board)
Yeah I would get a new A501 clone and put an AmigaKit Coin Cell adaptor on it so you can use a regular Lithium coin cell on it.