It is an electrical issue for sure, because if the flashing parking lights. If the tank wasn't venting, ignition issue, gas problem, the lights would not flash.
(1) I'd say it sounds like the Voltage Regulator is heating up, shorting, & killing the bike through the EHC.
(2) It could be a shorted cell in the battery. (mine has done that once as well)
(3) Could be loose battery terminals, or bad connection at the EHC plugs.
I would say that it is a 80-90% chance that it is one of those three things.
My bike did that same thing all three times that the voltage Regulator took a shit. One of the times the bike would not restart. The third time it would not start, only flash the parking lights, but I push started it and got it home. The VR was shot and it spiked and damaged the EHC. It averaged about 800 miles in between VR failures. Doing the same everytime.
All those BDM electrical items are gone now and no problems since.