67 Barracuda Turn Signal Dielemma

Yes, check the grounds for both the front and rear lamps. The pins in the multi connector on the back of the dash are also a suspect, but you say the dash was already restored. Still... maybe a good idea to make sure the instrument panel ground wire is attached, at least. There is a also a steering column ground wire that might affect the turn signal switch if missing.

As for the fuel gauge, it contains the voltage regulator for the instrument panel, so that is a possible connection. But if the PO installed a replacement aftermarket sender unit, you may just have to live with an inaccurate reading — the ones they sell as replacements are not calibrated for the A-body fuel tank and cannot be adjusted to be accurate over the full range.