No Start Electrical Help Needed Not Electrical Expert

I have power at all switches. The ones I was uncertain was the reverse and seat switch as I couldnt get the engine to crank with test wire that I bolted on the battery directly. I was able swap the brake and reverse as there the same to determine that the reverse switch was still good.

The only switches that should have power are the brake and pto.
Forget the rest as they work on the earth side and only affect spark.
The other switches should go to ground.

Just wondering if you ever got this figured out. I'm in an identical situation with similar Murray equipment (early 90'ish Murray - 38 in/11hp briggs strat). And the solenoid only clicks if I let it sit for an hour or so. Can't jump from car battery or from portable battery. I can get the starter to spin for a few seconds if I jump straight to starter with portable battery. Didn't do near the level of testing you did, but I know I have 12 volts from the battery to the starter with the ignition in the start position and all the safeties bypassed. Fuse looks good and passes continuity test. I also have 12 volts going into and out of the solenoid on the main positive posts (in from battery and out to starter). I haven't put the dvm on the ignition yet because ............ well ............ it's kinda difficult to get to ..... but I guess I'll go there next. Also haven't tried shorting the solenoid yet. There's a little bit of rust and corrosion on some of the connections but nothing that looks too bad.