I'd say that that was a pretty out there theory, but I've had a hell of a lot weirder things happen to me while trying to find the source of my torment.
I guess the only obvious trial would be to pull all the grounds off that side and bolt them to a wire directly to the (-) on the battery? If that fixed it, I guess you'd know. It's a long shot, but its not too difficult to try.
You might also (as long as we're talking long shots) jumper the important wires off the ignition switch (to where they're supposed to go) to rule out a short in any of them. That is definitely possibly a culprit
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Good Luck!