[TABOB]

The current wiring comes together in a plug so I assume I’m going to have to cut and splice to reverse the wires.

Cut and splice will do the job.

Alternatively, you can de-solder the existing wire from the motor, and replace the whole thing.
The connector is not necessary. You can solder the new wires directly to the pins.

If so do you know what gauge wire is is? Appears to me very thin gauge.

I have no idea what gauge wire it is, but you can eyeball it.
Using thicker wire will not do any harm.