Gauges and electrical gremlins

BE CAREFUL!!! There are many ways that solenoids can be wired/ manufactured.

If that is a "Ford type" solenoid, the unconnected post is the "I" terminal which does the job--ballast bypass--that the Mopar ignition switch does. The "I" terminal feeds to coil+ and gives ignition power when starting.

Or it can be "insulated base" and wired as you "think"--where the two small posts are the coil

Or it can be wired (rare) where the coil is internally connected to the big battery post, and the starter button grounds one small post to start (earlier Fords and some tractors/ industrial)

Is this a trunk mount battery? If not you may be well off to "convert" back to the factory starter relay. The key activates the relay, and it activates the starter solenoid. It is also incorporated into the neutral safety switch or 70/ later cars---clutch safety switch.

SO FAR AS gauges---usually pegging guages are a stuck/ defective gauge regulator/ IVR/ voltage limiter. If you do not have a Ralleye cluster, the IVR plugs into the PC board, a small rectangular box.