Cant Figure Out P0340 Issue

Well, you are not really "fixing" the problem if the code keeps coming back.
You have pretty much already ruled out the alternator, battery and the sensor.
Since it is "circuit" code, then you need to test that circuit wiring for good continuity and for being able to carry a load.
You will need a vehicle/engine specific wiring diagram and test the circuit end to end for high resistance, open, short to ground or short to power.
First test for 2 ohm or less resistance on the circuit end to end.
If that tests good, then test for the circuit to carry a load, IE, will it light a test light if the circuit has power.
Both of those tests will either confirm or deny a short to power or a short to ground.
If you have high resistance, fix the circuit.
If it will not carry a load, fix the circuit.
The easiest fix at that point it to overlay the harness (run a new wire end to end).
And one other thing to test for, terminal tension.
As in, does the wire connector pins have a tight fit to the sensor pins?
Loose terminal tension can lead to frustrating diagnostics and cause intermittent problems.

It will only go in one way.