Forget anything about the cluster for right now. OR THE COLORs, or the connectors. lets just follow some wires
You must have some positive all the time larger gauge wire running from the battery to the BAT. Always hot if battery is connected.
You must have a wire of some type running from starter solenoid to the SOL.
You must have a wire to the ignition coil (or computer and all the stuff on the LS engine) from ING 2. (NOT ING1)
This will get it cranking and a running engine and should turn off when key is moved to ACC ( or stop)
You then have some type of wire running from ING1 to gauges.
Acc can have anything you want running while your just sitting there but not running the engine like radio.
my guess without instructions is that the adapter cable you have goes on that middle switch of the three. The white connector goes on left three posts (SOL), ING1, ING2]
You guess correct here. The pink wire/power for gauges are run to IGN 1 +2. Thats why one stayed on and the other cutoff/lost power after ignition...?
Those two need to be on ACC. Key on/ Fuel and Temp check. I will work on it some tomorrow. Just super happy I did not damage anything.