Electrical problem starter won't engage even when jumped/hotwired

I have a 12yo Ryobi brand MTD made riding mower with 17.5 B&S engine 31c707 type 0154. Have tried bypassing the solenoid jumping starter direct from positive terminal with no response, just replaced the starter and still can't get any response from the starter at all. Have tried jumping from car battery and straight to starter also with no response. I know just enough about electrical and small engines to get into trouble. Something is preventing the starter motor from engaging. I heard a very faint click a couple of times on an initial connection but nothing consistent, usually I just get no response at all, no sparking, no clicks, nothing. Multimeter shows 12v going to the starter. There must be an electrical issue I'm missing, but what?