Disconnect the battery, disconnect the black wire from both coils, make sure the black wire isn't touching the frame. Turn the key to the run position and do a continuity test between the frame grounding point and the hot lead of the battery. If you get nothing, do the same test with the starter button pressed in. I suspect you'll get continuity between ground and hot on the "pressed in" scenario. If that is the case you've isolated the problem to either the key switch, starter safety unit, starter relay or the wiring coming back from the start button. Unplug each unit until the condition goes away. If you don't get continuity either way try the same test with the battery connected, that will supply power to the relay and send current to the starter. If you get continuity this way, you know that the problem is the heavy gauge wire past the relay.
Good luck.