Did that solenoid ever work correctly? Or, is this engine/rig/harness new to you? Continuous clicking from the solenoid usually means a bad connection or a bad battery. But, something about that solenoid does not look original, and it may be the wrong style which might explain why it does not work properly. Needless to say, If this solenoid worked "OK" previously, this theory can be ignored.
Please be careful if you are going to jump the large solenoid terminals, pretty easy to short the pliers to the junction box case which I’m pretty sure is grounded. If the engine cranks when the large solenoid terminals are shorted, that rules out the battery/starter and large cable connections.
If the engine does not crank with the large solenoid terminals shorted, then I would start by having the battery load tested, just cuz it’s charged doesn’t mean it is any good. Doing a voltage drop test with a decent anolog voltmeter might help pinpoint the problem also…