This particular insulation is rated for 1000V and the shielding is braided making it pretty thick. For those wondering how I got to 16 gauge, here is the math:
800W spindle / 110V x 1.73 = 12.58A - EDIT: I have since learned that this isn’t quite accurate. The correct math is this:
800W spindle / 110V / 0.75 power factor (approx) / 1.732 (3 phase magic because you are using 3 conductors to carry the current, not 2) = 5.6A
This is simplified and I am not the person to give more detail. An electrician will have to go into more detail