You can call Lance, they may have the answer you need, even though you may not have a new TC.
On my 1988 Bigfoot, the vent itself did not have wiring, but it had a junction box in one of the overhead cabinets across from the vent. Actually, it did not even have the hole cut for the vent. I had to find the framing and the hole. It was framed. I found the factory left a slot from the framed hole to the box so you could fish the wires through.
If you do install the A/C in place of the fan, you might consider moving the fan to the bathroom. It will do a much better job than the original bath fan.
Wayne