Not to say anyone is wrong but to me a double throw, single pole switch (On-On) is the way to go.
Some wire, some fuses and you are good to go.
First find the reverse switch on the trans, lift the wire that goes to the reverse lights.
Cut this wire and extend both sides to reach the Switch.
Attach the wire going to the lights, the load, to the center pole of the switch.
The wire that is still attached to the trans, attach that to one of the other two poles.
Test - with the truck in reverse and the switch in one of the two positions available the lights should be on. If not double check all of the wiring.
Next step, run a fused wire from the battery to the empty pin on the switch.
Test - Flip the switch to the other position and the lights should work.
Position the switch so when the trans is switching the reverse light the dash switch will be in the down position, sort of an Off Position; when up the manual over-ride will happen and the lights will be on.
This setup can be changed but as is it will work with LED reverse Lights and OEM reverse lights of 35 watts and lower.
If you want to wire up some high wattage lights 55 watts and higher, add a relay. A relay will allow the light to burn their brightest.
Relays are easy…
The load wire from the manual switch, the wire from the middle pin, this should go to pin 85 on the relay, pin 86 should be grounded.
Run a new fused power wire from the battery to pin 30 on the relay and then from pin 87 to the lights.
Run new HD wiring, 12-ga minimum, to the lights from pin 87.
12 gauge wire will handle 20 amps so it should cover almost any pair of lights out there except the older 130 to 150 watt lights, these need a 10-ga power wires.
Fuse all power wires and use wire gauge based on the total amperage of the light draw; double it if there is a question.
Always get good grounds, bare metal for contacts or run the ground wires back to the battery; more wire yes but usually less ground problems.
So this is confusing… think it through, one switch with three pins.
One common , the lights goes center.
Two power sources (sort of) two other pins, one source to one pin and the other to the other pin.
Use large enough wire or thing will burn up besides your truck.
Fuses should be close to the power source or else when shorts happens the power will not be cut off close to the battery and again a burnt up truck.
OK too much, I will get off of the box.
IMHO you do not need a special circuit for this setup, there will be no feed back since the switch will be in one position or the other.
There is no so called “Off” position because the switch will usually be in the Trans Reverse Position or auto, sort of an off position and in that position the trans will handle the power switching.
One more thing, if you like indicator lights, get a double pole switch, one with two sets of connector on the back.
One row for the power control and the other row for indicator lights.
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