Pos a year or more ago I had visited with a gentlemen with the same problem because mine was/is still doing this . I have never been left stranded as it will finally crank
Anyway he had told me he had his at two different dealerships and each place had it for a couple of weeks and neither could find the problem
He did say and I had read an article about the same thing,that there is some sort of headlight safety switch that kicks in to keep the headlights from running the battery down and if it malfunctions then you get the click click
I have no idea if either statement is fact as I do not know the guy and I did not verify the article
The thought is that maybe it is not in the start circuit but something else that does not close and allow it to crank