Well, here's what I found. Removed seat, side covers, Bearclaw (now I get it!), slid tank back. No sign of burnt wires at the plug after disconnecting, so reconnected the plug. Secured the clutch at handlebars, turned on ignition and got the same intermittent connectivity and starter relay click, still no start. Maybe the starter relay got fried? Dealer does not have a relay in stock, but thinks the ignition module may be toast. He'll check to see if he can get one made to my key on Monday.
Removed the windshield, ignition cover, loosened the plastic inside the Bearclaw, disconnected the plug and pulled the ignition wires out to the front. Removed the two bolts holding the ignition module to the front (difficult from underneath), then had to move the headlights up to get the module out. Reconnected the plug and held the wires in a position to maintain contact, and got the bike to start. Relay is ok. When I let go of the wires, the bike died. When I shook the module, something rattles inside. Must be the broken connection or solder. New ignition module is $177. At least I'm saving on labor costs by doing it myself. Plus I'm getting to know the bike. Should be back on the road in about 2 weeks.
Thanks all for the suggestions! While I've got it apart, I'll order up the EB relay and install my newly procured MotoLights. And probably get a GPS power line too. Gonna take the C out tomorrow, and meet Jack and a couple of Chromehead buddies for breakfast and a ride.