Four terminal solenoid, so you should have 2 heavy wires (one from battery, one going to starter) and two smaller wires, one should go to ground (does it). The other wire is part of a series circuit that runs from the battery, ignition switch, seat switch and PTO switch and possibly a switch on the brake. These switches keep you from starting out of the seat, with the PTO engaged and with the brake off, any one of them not working or a wiring fault will keep the solenoid from engaging. If you run a wire from battery positive to the non-grounded side of the solenoid coil, does the solenoid try to engage?
BTW - I had an intermittent start problem on my Bad Boy mower, turned out the bolt on the positive battery terminal had loosened up, made good enough connection to run the mower, but didn’t always pass enough current to crank the starter.
BTW - I had an intermittent start problem on my Bad Boy mower, turned out the bolt on the positive battery terminal had loosened up, made good enough connection to run the mower, but didn’t always pass enough current to crank the starter.