True.
You'd think after having the starter in my beat up car do something interesting that sounded similar, I'd have thought of that.
This really sounds like the battery has good juice, the switch and solenoid are ok, but something else needs a breather before it'll crank. If it was cranking, but no spark, I'd agree with a fuel problem. However, the fact that it's giving a "click-click-click" kinda thing sounds like a starter issue somehow. That'd be a ground, fried primary windings, heat soak from the exhaust (too hot exhaust or a dying starter, either aren't good), ect...