The third post is ground, and if you've lost that, then the symptoms do fit.
The electromagnet on the sender side pulls the oil needle down and pulls the temperature needle up. They're opposite. These are pulling against a constant amount of magnetism pulling the other way, and that's what you've lost.
if you take the gauge apart, you'll see two ballast resistors built into it that control power through that circuit (but don't do that, I guess). So the ballast on one side competes with the sender on the other side (literally) of the gauge, but the sides are reversed on the oil pressure and the temperature.
Most of the bulbs are connected to that instrument panel ground circuit, and the tach is too. It's the most widespread circuit on the whole thing.