EDIT LOL I was typing..................
May or may not be the starter relay, "how it works."
Notice you have two flag/ push on terminals on the relay. These are the relay coil. The huge stud gets power from the battery, serves as a junction point for other components, and is one of the relay contacts. The other contact is the "square" terminal which feeds down to the solenoid.
If you can get the starter to crank when you jumper the two bare large terminals on the relay, the relay is getting power to the contact and the starter sol wire is good.
One of the flag terminals feeding the relay coil gets power when you twist the key to start, but it needs a ground. On automatics, the remaining "flag" terminal has a wire going down to the center contact on the neutral switch on the automatic to ground. On a stick that wire goes to the clutch pedal mounted switch
So take a meter/ test light and make sure the relay is getting power from the key in "start" and make sure the neutral switch is grounding. You can remove that wire, and ground that flag terminal temporarily to test it
HOW THE KEY works
Normally when you twist the key to start, the key also kills the "run" voltage to the ignition. That power is supplied by (older models) from a different contact on the ignition switch, feeding power in start to the coil + side of the ballast. On newer rigs, the start relay has a FIFTH terminal and it does that job, instead.
As said above, when you jumper the starter, that circuit does not engage, so you get a weak spark. Most vehicles, tho, in good shape, and tuned up will start that way
