To use a relay, you will need to find the pinout diagram on the net. You will need a standard 30amp relay (found in most auto parts places), some female crimp-on connectors, and some good 14 gauge multi-strand wire.
You will need to cut both of the wires that goes to the reverse light bulbs. Better yet, if there is one wire that then splits to both bulbs, cut the single wire. If you must do both, you will need to insulate one of the ones that goes back to the wiring harness to prevent a short, as you will only need one wire.
Now, install the existing hot wire to the hot lead of the relay. Install a wire to the ground lead and then connect the other end of that wire to the car's sheetmetal as a ground. Make sure you have a good clean metal connection. If you don't, you will have trouble with it.
Now, you will need a 12V wire from the battery to the relay's NO (normally open) connector. A fuse as close to the battery as possible is mandatory to prevent a fire if there is a short!!!! For two 55 watt bulbs, a 10 amp fuse is cutting it pretty close, but I would start there and move to a 15 if it fails.
The opposite side of the NO connection should go to the lights.
Now, when you turn on the reverse lights, the relay's normally open internal switch closes and connects the reverse lights to the battery with a fused connection that allows the correct amount of current flow without over heating your wiringing harness.
Can anyone else add to this?