Would have thought a model of that age would certainly have a small cube shaped starter relay which should make a faint click if operating. This sound will usually be masked though by the louder clunk from the piggy back starter solenoid which both engages starter pinion and applies power to starter motor itself. The old mechanics trick was to short between the two large terminals at back of starter with large blade screwdriver to bypass solenoid and prove starter itself spun.
If flat battery or poor earth connection is to blame solenoid would usually click in rapidly repeating fashion. You don't mention that happening so suspecting solenoid as you do would be a good first call. Bosch ones I know can be replaced individually but for Ford ones it may be simpler to replace whole unit.
