Relay Basics (for the common, 30A, "1"X1", black "ice-cube" relays)
A relay is just a remote switch that makes a low draw source to switch a high draw device (like making the reverse lights power from the factory turn-on big lights)
For some reason I don't know, almost Everybody has continued to use the same label for the relay connections (I think it was Bosch who first did this) BUT if you look at most relays like the ones we're using, you'll see a small schematic on them with 85 - 86 - 87 - 30 (and sometimes 87a).
What the schematic shows is that the coil (a little electromagnet) is between 85 and 86. When current goes through them it pulls the contacts from 30 and 87a (called NC for Normally Closed) to 30 and 87 (called NO for normally Open) and gives you the choice to have something either turn-ON or shut-OFF with that little electromagnet coil.
SO,,,,, let's say you GROUND 85, and take the reverse light supply wire your current lights get their power from and connect it to 86.
Now, when they come ON, the contacts in the relay connect 30 to 87. This means if you have a (fused, please) 30A wire from the battery connected to #30 on the relay, you can draw up to 30A of power to anything connected to 87 (like BIG lights
The relay can be located anywhere in the system so make it easy on yourself and put it where the the source wire that trips the relay (in this case the factory reverse) is close to where the new, power wire, will be - like around the back bumper area.
Pay attention to your ground, make it scraped clean & greased to a solid ground (frame, sheetmetal, or, if you're Sure, a factory ground wire that is)
Relays are SO USEFUL on So Many ways and once you start using them you can't get away from them!