Remote turn on wires are just a switch. (If you thought of it like a home stereo, they are the power button on the remote control, if your setup didn't have a plug and your choices were to unhardwire it, or push the easy button). They are VERY small, usually 100-300mv. They usually include something like 18ga. You could technically use something as small 32awg, but that small is not going to work well if you are making a run from your head unit to the amp, (just too delicate and easy to break). 18awg is usually the easy answer because it's cheap, small enough you can run it anywhere, and not too small where you might accidentally damage it. 14-20awg is fine if you already have it, or that's what's available. Some amps say 16-18 because that's what fits in the terminal. There's some flexibility in there, but 16-18 is just the best overall choice.