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You can go to Azone and buy a plug in 7pin harness that will tap into your rear wiring harness, and in doing so will give you the 7 pin plug. It will include the addition wires for the other pins(12v power, brakes and reverse lights).
They also make a version that plugs into your truck wiring harness under the back and it a much cleaner install. I used this version on my '89 F150. I think it was Husky brand? It came with the proper factory plug to fit my truck.
Since your existing 4 pin is not working properly, it might be better to replace it with something better. How is your 4 pin installed? Factory or someone just add it(bad connection)? Could be a bad wire, since your truck lights work correctly?
BTW, breakaway brakes are mounted on the trailer(if need be) and has nothing to do with the 7 pin connector. You can take the 12v pin and add a charger to the breakaway battery to keep it charged(or a deep cycle used for a winch or lights).
My '95 F250 came with a towing package - this meant I had two 4-pin round harnesses that were meant to hook up to a 7-round plug, a 6-pin rectangular connector on the dash for hooking in a brake controller, and two 4-pin round harnesses just forward of the brake booster under the hood where a relay package could be added. I would check for those plugs, just in case - you may already be fully wired and just need the end bits.