1996 4Runner V6 A/T 4x4

Removed starter, tested it straight to the battery and it spins. Put starter back in, no start even when powering it directly to battery with jumper cables. New contacts and plunger in starter. New battery at 12.75 volts.

Please see this 3 minute video I made:

 

I don't expect that fine guage wire and alligator clamp are providing enough power (remember, power equals volts times amps?)

You're missing half a volt just thru your hotshot, which appears to be two to four times the carrying capacity of that wire with the alligator clamps. What are you getting on/at the starter solenoid, on the far end of that alligator setup? You can actually measure the voltage drop and not have to do any math by attaching one meter lead to the battery post and the other to the starter solenoid. 😉

 

Yes, try this.