The wiring should have nothing to do with it. I've got the starter all the way down to just the red cable from the battery and the starter mounted to the flywheel, all other wires have been detached, for testing the setup. It should at least kick over when I push the solenoid button, period.
As far as how long to fire up, the previous 2 starters kicked over immediately. The starter issue just started yesterday. So I swapped the 2 week old starter out for another one and the newest one isn't kicking over either.