If using an electrical wire gauge, is the gauge placed on only the copper or does it include the insulation to determine which gauge the wire is?

I guess I don't understand your question. Why don't you just read the information that is printed on the wire itself (assuming of course that it can be read).

Insulation depth can vary. The gauge should be placed on the copper or aluminum itself.

Can you take a moment and tell me what exactly you are trying to figure out, please.

Wire gauge or size is of the conductor, regardless of the insulation.