You do not want to use romex or any solid wire in a vehicle. The flexing and vibration will eventually break the wire as it is not designed to be flexed. THHN is industrial wire. If it is solid wire, don't use it for a vehicle or ATV, same reason. Stranded version would be ok but it is also not rated for it. (it won't be flexing that much in a vehicle) MTW wire would be the best bet, but for what your doing if the THHN is stranded, go with it. A lot of charts show voltage drop over length but that is for AC voltage. DC voltage has a higher drop rate over distance. My general rule is I bump up one gauge for what is needed.

Yes I have 14 awg & 10 awg stranded THHN CU and of course 12 w gnd Romex (solid of course). Tempted to use Romex cable but terminal connections are difficult to look good with solid.

Use 12 gauge , even 14 would do.. 10 gauge is way overkill. Your choice whether to run ground wire back to the battery or ground to frame.. Either would work, but my preference is to run both wires from battery to socket. There is a wire chart in the download section showing capacity of the different gauges and wire lengths.. I generally use heavier gauges than those shown for my wiring to be sure to minimize voltage drop over distance.