Question about voltage limiter

OK. Maybe place a piece of tape over that LED? In my mind, standing green is good, flashing red is something wrong. They must have had security system in mind ( that's typically a flashing red ). Dang if I know. Anyway...
There's a ground jumper on the fuel line at the sender. It can cause gauge changes as it moves with vehicle vibrations. That ground path is through the fuel line and the now rusty clips attaching it to the chassis. There could have been a actual wire attached directly to the frame but it was meant to serve 10 years, not 50+.
If the fault is in fact the sender, best to have original restored. Aftermarket replacement senders are wrong. Good luck with it.