But I narrowed down the signal changing to the output of the wiring from the sender right?
Not as I read it. See my post #20
The true test is removing the sender from the circuit. You must first test a solid ground, then with confirmed ground test sender wire to guage. This means using a known good ground (both sender ground lead and battery) and known good 12 volt (+) lead.
In your post you say you simply remove and reinstall leads at the sender. This doesn't definitely prove fault of the sender.
As I mentioned earlier, if you're still experiencing an audible alarm when the engine is running you must use a compatible diagnostic tool in order to ascertain the active fault