Its not the starter. Remove battery negative cable-both ends and clean cables and frame where cable goes. A new bolt and re assemble.
As you mentioned the lights go out when you try the starter, thats a circuit opening. Battery will do that-they have the potential to explode if they arc internally (happened to me once) so please be careful.
When my tractor did this, i removed battery and cables and cleaned everything.
Its been nearly a year without a hiccup.
Could remove starter and test with jumper cables on a different battery.
Keep us posted, would like to know what solved your issue.
I will be trying that tool junkie, thanks!