Starter clicks using the key, engine starts by jumpering the relay

Let's review and think here................

If you jumper the two large exposed terminals at the relay, AKA the big stud and the "square screw" and if the starter cranks the engine "normally," we know the following:

The battery, battery clamp connections, main battery cables, connections at the block ground and the starter, and the starter itself are all good

If so, it's all in the starter relay and related. Might be the relay, or a bad connection in the relay coil wiring. "The path" is: Ignition switch---twist to crank--yellow start wire--out through the bulkhead connector--EDIT(??through seat belt interlock?) -- to the flag/ push on terminal at the starter relay--through the relay coil--out on the remaining flag/ push on terminal--down the firewall--to the transmission neutral switch.

Any part of that might have a bad connection/ low voltage/ drop and of course the relay itself

One way to separate the wiring from the relay as a problem is to alligator clip a ground wire in place of the NSS wire and see if it works (BE CAREFUL it is not in gear!!)

If that changes nothing, then jumper direct battery power to the "start" terminal of the relay by pulling the yellow wire off and jumpering bat. power direct to that terminal, making sure,of course, that the NSS terminal is in fact still grounded.