So, tank came off today - it looks as though there is no damage to the cabling for the FI. I've added padding to the potential wear areas.
I tried to look at the connection for the regulator rectifier, but struggled to get it off.
Washed the bike with a pressure washer (always do) Bike started no problem.

Battery was still good after 36 hours.

So back to square 1 - not sure if it's cold or wet that causes problems....