I have to chuckle
When we bought the SkipperLiner we had no keys for the flybridge ignition switches, so I bought a couple of new ones. And I didn't put the rubber covers on... I found out the hard way that I should have, and I'm here to tell anyone that YES, water will indeed wreak havoc with switches-- In the middle of the night during a drizzle, the starboard engine started itself up. Scared the bajezus outta me! Lemme tell ya, the thought of someone stealing your boat while yer sleeping in it is NO fun! When I found the problem, I had to push the stick past neutral to kill the power to the starter, which also stalled the engine. Too bad I didn't do that with the port stick because less than an hour later the port engine also fired itself up!
SO-- not sure if water is the OP's problem, but if there's ANY chance of water being anywhere NEAR the electric connections or switches, that may be the problem...