Rallye cluster gauge issues - 67 Barracuda

you said you checked a fuse. There isn't a fuse other than the fusible link. 2 of blue with white tracer in one terminal at your ignition switch. One goes through the firewall to feed the charging system voltage regulator. The other goes to the round harness connector on inst' panel to feed gauge voltage regulator.
About the post above that shows opening the gauge and disconnecting the 12 volt supply to the limiter. It doesn't say anything about this gauge with limiter being chassis grounded. So assuming the limiter still has continuity through it, The 5 volts supplied by another source will back feed through that limiter to ground. So that limiter is wicking away some portion of the 5 volts, as if it were a 4th gauge.
No one even needed to open a gauge to disable a limiter. Simply lift the gauge from the housing and cover the small piece of metal on its backside with electric tape to isolate it from ground. Take the blue with white tracer out of the round connector and route it to any substitute regulator mounted anywhere you like. It doesn't have to be on the back of the inst' panel.
The unit from Real Time Engineering is the one to buy. It costs more but... it includes ground fault protection. That little 7805 chip does not. If it looses chassis ground, 12 volts goes straight through it and out on the wire that should be only 5 volts. That will fry all 3 of your gauges. The RTE unit has LED indictors on it so may as well mount it where they can be seen. Nowhere to mount it on the back of the rally panel anyway.
A guy named Rick Erinburgh (or something like that) first published this "open the gauge" procedure to a Imperial website about 20 years ago. He hadn't look at it close enough. Then others propagated that info without doing their own study.
In the end, I hope you find only something simple,, a loose pin at the blue with white, or the fuel gauge is a little loose at its mounting nuts, limiter lost its ground, you didn't need any of this info.
If you do determine a substitute regulator is needed and you'll convert the amp gauge to a volts gauge... the blue with white should also feed switched 12 volts to the positive side of the volt gauge. You will need to add a ground wire to negative side of a volts gauge. There is a proper method to do that too.
Somewhat of an update: So I still haven’t had a chance to do any meaningful troubleshooting. I verified all ground connections and removed the +12V supply to the tach from the blue wire with white trace. You’ll remember I mentioned in the original post that this is where the old tach’s backlight feed was tapped, and I used it to feed power to the new tach, which may have been a mistake.

Fuel, temp and oil gauges are working at the moment, but the fuel needle is still tending to ‘wander’. Tach is the same (visibly getting power, now from the fuse box, but not responding to the tach signal).

I suspect my issue may have originated with the faulty tach. I’m a little unsure about how the tach being fed from the blue/white wire may or may not have affected the voltage limiter inside the fuel gauge. You said the blue/white feeds the limiter, but the schematic in my ‘67 service manual shows it going to the brake warning light.

Again, no real troubleshooting accomplished. The stuff I mentioned in the prior paragraph is based on gut feeling. Any thoughts?