Ignition switch or solenoid is bad.I know bad grounds can often be the source of the problem. Been through that a few times. This "seems" to be something else though. I've already removed the frame ground and reattached it, and the battery post and terminals look brand new. It has the automotive style round lugs and everything is tight and clean. Starter spins and cranks the mower easily when I run a small positive wire directly to the spade on the solenoid. Just touch the wire to it and it engages. Getting the same 12V charge from the wiring harness (when key is turned to "start" of course) and nothing but "click"
Somehow, the 12V + from the wiring harness is different from the 12 V + direct jumper wire
Edit: would also like to add that "sometimes", like 1 out of 10, the thing will actually crank with the key. Most of the time it will not. Although it will click every time.
First thing I look at is grounds. Most people neglect it or overlook them. They attack the + wires all day.