I can start the mower by jumping the battery and ignition terminals on the starter solenoid. So solenoid and starter seem to be OK. And all safety switches are temporarily bypassed, thus they are not the problem.
Upon further troubleshooting, I find that the wire running from the start relay to the starter solenoid (red) goes from 0V to 12V upon key turn, but only when disconnected from the solenoid. Upon connecting, I get no appreciable voltage reading at either end on key turn - thus no start. Puzzling to me. Make any sense to you?
Still think it might be a bad relay? The start relay does not seem to click as hard as the kill relay for whatever it is worth. Before spending the $10-$15 on a relay, would switching out the start and kill relays as a checkout work?
I notice that 12V five terminal relays appear to be sold in local auto parts stores. Same part? The look identical. Same numbering a the terminals I believe.