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

A remote switch on Mopars generally just replaces the screwdriver, BUT you can use it in a second way to test the coil circuit

So using a screwdriver cranks?

Now test the relay. Hook one clip of the remote switch (or a jumper wire) to the terminal of the relay after you remove the yellow(?) start wire. Hook the other end to battery OR to the big relay stud. Does it crank? NO?

Now test the ground end of the circuit ---the NSS switch circuit--by jumpering a screwdriver or jumper wire from the terminal on the relay where the NSS wire connects --jumper that to ground and press our remote button. Relay should activate and crank the engine

If it does, relay is OK and you have a wiring problem

If not relay is likely bad