Car won't crank, Guage lights flash, and how do I pull my starter?

I agree with all that has been written above.
Approach it systematicly.
to wit -
1. Battery has enough stored power? Flip the headlights on briefly. Dim or strong. Dim - recharge or get new battery. Unsure - load test.
all I get is a click from the starter, and no solenoid rattle.
This can can happen when the battery is weak.
2. Connections? Disconnect the battery ground, then the positve terminal and meake sure they are clean. Make sure the connections at the relay are good. Then check the one at the starter with the replacement terminal. Wires should be firmly crimped to the terminal. I know, you wrote they are OK. Just going over it.
3. Relay or starter ? On a '66 the relay should look like this
upload_2019-11-16_8-4-54.png
When the key is in Start, there should be power in wire going to the diagonal terminal in the corner.
If the terminal in the other corner is grounded, then the circuit is completed and the relay closes. On an automatic, grounding is through the neutral safety switch. Since you hear a click, at least that part of the relay is good.
When the relay is closed, that connects the battery to the middle terminal.
upload_2019-11-16_8-11-23.png
A crude way to jumper those two is using a screw driver with an insulated handle. Do not touch any body ground!

When you go to remove the starter, disconnect the battery, then the heavy and small wires at the starter.
One attaching bolt is a long hex head machine screw, but the other may be a nut on a stud.
Access them however is most convenient to you with the tools you have.