Might just be worth checking the wiring. I've had intermittent starting from a poor connection from the ignition wire at the starter. Its possible that the love taps are also (temporarily) resolving a connection issue on that circuit. It seems unlikely in this situation, but I've also experienced intermittent starting when the earth cable at the battery wasn't refitted properly by a 'storage guy'. I'm sure others with more experience will be along shortly with some other things to check before pulling the starter.
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