Solenoid Clicks by itself?... lawnmower won't turn over.

Hello new member here and I am hoping someone has seen this problem before so I may get lucky enough to fix this issue on my own. Here it is.

I decided to spray down my MTD (Huskee) rider w a Briggs and Stratton 12HP engine with a garden hose a few weeks ago because it was dirty and hadn't been washed in years. After washing it, I started it up, drove it to the shed, and parked it for the next week until I needed to cut the grass again.

Fast forward to the next week and the battery is completely dead. I charged it up again (battery is only 1 year old) and upon trying to start it, nothing happens, no clicks, no nothing. While scratching my head wondering what is wrong all the sudden I hear "click.. click" from the solenoid, on its own.... with the key OFF.

Here's the funny thing, the solenoid clicks every minute like clockwork BY ITSELF with the key off (this is what caused the battery to drain no doubt).

This is hopefully the thing somebody will notice, and be able to pinpoint where the short is occurring. I believe it is somewhere in the wiring, but the repair shop said it could be as much as $200 to replace the wiring harness. I just can't afford that right now. I could go out and buy a wiring harness and do it myself, but to my knowledge there is more than just one wiring harness where the problem might be coming from.

What I did
Cleaned all connections, battery ground to chassis, all terminals I could get to etc.
Sprayed contact cleaner inside the wiring harness for the ignition, and any others I could get to. No help.
Jumped the solenoid with a screwdriver and the engine turns over, but no spark (yes, key was on).
Replaced the ignition switch, no help
Replaced the solenoid, no help
Battery is charged fully at 12.8V
As soon as I hook up the battery I hear a click. Then the solenoid will click twice every minute without me doing anything, and with the key off.

Once again,
MTD Huskee
12HP Briggs and Stratton engine

Thank you for any help you can give!!

Tripp

Maybe the hose down led to some contamination getting into the keyswitch? Perhaps it's causing some current to flow that's just on the edge of being enough to activate the starter relay...

There's also a chance that the same contamination is preventing spark (in the key switch, or one of the safety switches). If there's a connector at the key switch, you could disconnect it and see if there's any change. But re-reading your post I now see that you replaced the keyswitch, hmmm.

Are you certain that this all started with the wash? Could there be some chafed wires that are making intermittent contact? (like shorting to the frame)

Can you positively identify where the clicking is coming from?

If the starter relay, what happens when you remove the low current wires (the thin ones)?

If you can find a wiring diagram it might help (in the manual maybe?).

If you don't get a satisfactory answer here, try this http://www.perr.com/phpBB3/viewforum.php?f=14&sid=e1db222ced28ecd43a572d361addda8e

Good luck!
Bruce