someone else said. grab the light, and just hook it up directly to the wiring harness at rear of truck. with some jumper cables or like. and see what happens.
jumper cables being. a couple pieces of wires. ran from wiring harness to cables on light. and piece of tape around each connection.
if need be have a second person help you. as in, applying brakes, left and right turn singles, flashers on/off. turning on / off tail lights.
just a side note, i assume you have ample power for additional lights. but you might have a cheap extra flasher unit. for tail lights. that may not have enough umph to run all the extra lights.
the idea of running lights off the wire to the trailer brakes. has me on edge. just does not sound right. i mean technically it could work. but doing so could cause the brakes not to work correctly on the trailer. or rather make that, the brakes would not apply themselves as good as they did before if you ran light off of the brake wire.
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on another note:
if you are placing this dead center, i would just use it as a marker tail / brake light. and forget idea of turn singles in it. if you had 2 of them and placed each one on left and right side, OK. but dead center. I don't know about the idea of using it as turn singles.