Tail light stay on
Eventually you may want to put the original headlight switch back in.
The reason is most replacements have 20 amp circuit breakers instead of the 15 amp breaker it should have.
That is an aside.
In addition to the diagram in the Service Manual, you may find the master tech conference helpful.
For example this one is about reading and using the electrical diagrams.
https://www.web.imperialclub.info/Repair/Lit/Master/247/Cover.htm
Lets look at how the circuit is supposed to be, and what is shared and what is not.
L7 is the Rear Tail Light circuit.
I beleive you will find the connector for the body harness behind the driver side kick panel.
Circuit L7 is position 3.
If you disconnect the halves and the instrament harness side has power, then its onto the next connection.
According to the diagram, the next spot is the headlight switch.
Here it joins with the front parking lamp circuit L17.
My guess is there is something wrong with the wiring because if terminal R is hot (has system power) then L17 would also have system power.
Power to the parking lights and tail lights comes to the switch via the B-2 connection. Wire L8.
L8 shares a fuse with circuit D31, which feeds both the emergency flasher and goes to the brake light switch.
The fuses fed from the "battery feed" are always hot when the battery is connected.
Seems like you are looking for a cross wire short, an incorrectly connected terminal, or as earlier suggested brake/turn circuit.
If you find its a terminal, they can be removed from the plastic hosuing using a cotter pin, a hairpin, or actual proper tool.