Yes, it's fuse #32 and also feeds the horn relay, so if the horn works, that isn't it. Your gen1 doesn't have "smart" charging so there's no ECU which turns it on and off, you should be getting around 14V anytime it's spinning. There is an intervening connector, E6:F123, in between the field fuse and the alternator. See CHG-16 here for your wiring diagram:
https://www.nicoclub.com/service-manual ... %2FCHG.pdf
Your best diagnostic path is to check the voltages at the alternator. The pink wire on pin 4 must have battery voltage at all times, that's the field wire. If there's voltage at the fuse but not at Pink, you have a wiring issue between the F&R Box and the alternator. If Pink is good, with the car running, measure between main alternator lug (red) and battery+ (black). You should see a difference around +50mV (0.05V) if your wiring is healthy and the alternator is putting out. If there's a large positive difference, 2~4V, then the alternator is putting out but something is disconnected between the alternator and battery. That isn't necessarily a fusible link, those battery cards are occasionally known to crack invisibly inside the plastic. It also could be that your battery lugs needed more than a cleaning. Voltage drop will tell you where the problem is, trace back along the path and find the spot where there's drop on one side but not on the other. I.e., if there's a 2V drop from the alternator to the battery post but a 0.05V drop to the battery lug, the lug is corroded. If there's no difference or the difference is negative, your new alternator is defective.