That car in your driveway is a heavy drain on your bank account between gas, insurance, and routine maintenance, so adding towing gear needs some care. Late winter is the sweet spot for this project because shops are quiet before the spring camping rush hits and demand drives up labor rates.
You should negotiate the price of the custom hitch and wiring harness installation with the mechanic before you ever mention how you plan to pay for it. Keep financing separate from the purchase price so you do not accidentally trade a lower labor rate for a high-interest monthly payment plan.
Remember that the intro window is a hard deadline and not free money, so if any balance remains when those 15 months end, standard interest rates will apply to what is left.