I've seen starter failures where the motor seizes and the bendix still engages causing nothing more than a clicking noise. If you can identify where on the tractor the clicking is coming from that may also help ID a source problem. A seized starter will create tremendous amounts of load on the battery, if you can get the voltage of the battery when someone attempts a start, while they're in the start/crank position the voltage will drop significantly.
In inspecting your wiring, wirebrush all your main leads and battery terminals. I've also seen them snug enough to seem fine, but after a while a fine layer of oxidation/corrosion occurs preventing good contact. I've seen it where they appeared clean, but running a wirebrush over them shined them up and all was well. As a "down and dirty" method, you can also just loosen stuff up enough it will snugly rotate, and give the cables a twist back and forth a couple times and tighten it back down.