1968 Barracuda 383/4spd

sender with oil pressure shows 19 to 22 ohms. that should move the needle to about middle of range/gauge screen. Shorting the wire to the block is zero ohms test. That can make a faulty gauge do what normal the 80-10 ohm signal would not. Zero ohms should take the needle to its max position and hold it there. A fluctuation is not normal. The beam should not heat and cool fast enough to fluctuate the needle if the limiter is working properly.
What I would do... short the temp sender wire to the block. If this needle fluctuates also, the limiter output is the problem.
Your fuel gauge has a slither of metal on its backside that sits on a unpainted spot in the housing. This provide ground path for the limiter. A few owners have found a poor contact here to be the problem.