No fuse originally (on a TR3A), but it's possible someone has added one.
I would start checking voltages at the relay unless you've already got the tunnel out. IMO the relay, lockout switch, dash switch, and solenoid are about equally likely to be the problem. Oh, and FWIW, the overdrive circuit is supposed to be connected on the battery side of the ammeter, so you wouldn't expect to see anything happen on it anyway.
FWIW my "intermittent" lockout switch proved to have been improperly adjusted, by a "professional". Removing the "as required" gasket fixed it right up.