Couple of things to check:
- Is the earth wire on it? Looks like it was as there was a nut loose in the pic (top left).
- When running is there 12-14v at the large red wire on the back of the alternator? Use the battery as an earth, then the block as an earth, then the alternator housing. If 12-14 on some and not others then chase earth straps.
- Is there 12v at the small wire on the alternator when running?
While you are in there check the rubber bushes for the lower mount and top adjuster, the car looks in good shape so you have likely already done this.
If you get a replacement I suggest going for an 80 or 100 Amp unit, that would most likely have been a 55A.
