1985 FC 35 Generator start up

[ssyd1]

I have my FC now a year, just about ready to hit the road.Very happy
with my BB. Need help with my generator. Twice now the generator as
started up on it's own.Once last February ( during a very rainy day )
and again now in March ( again a rainy day )When I shut down the
generator the starter keeps running.Had to diconnect all power to
starter.Could the starter solenoid be the problem or is it some other
electrical problem.Thanks to all for you help.
Mario 1985 FC 35 L.I. N.Y.