The bigger blue box is a SPDT relay. That stands for "Single Pole, Double Throw".
Click here if you need to know how a relay works.
Look for a very small relay. The load (CheeseBox) is very small; probably much less than 1A. In general, the smaller the rated load of the relay, the less current it will need for the trigger (to activate the coil and make the switch). This would be especially important if you have a car that can detect burnt out reverse bulbs. I'm not even sure that you could find a relay that will work without triggering a burnt bulb signal in those cars. By adding the relay, you change the resistance/current in the reverse lamp circuit of the car. A smaller relay will minimize the change, though.