Bad Starter or Starter Solenoid?
Here's how to separate the starter relay from the starter solenoid
Under the hood, ID the "push on" wire going to the neutral safety switch. This is usually "not" yellow, and it goes right down the firewall, over the trans, and down to the switch on the trans
The remaining "push on" wire is the start wire
Remove the start wire, make sure the trans is in park / neutral. Jumper (screwdriver, clip lead) from the large exposed battery stud to the small push on terminal you just unhooked
A small "click" there is the relay.
Now, take your screwdriver and jumper the two large exposed terminals on the relay. A good starter should pull in with a loud snap and turn over. If you get sparks, but no snap, it's for sure "down there."
I'm REALLY surprised you cannot get a mini starter out of those headers.