I seem to recall that Volvo uses 2 items for the wiring, the first is the connector box, the second is the wires to the trailer plug. You could look at this:
https://www.etrailer.com/p-119179KIT.html

Volvo rates it's cars for a 3500# max towing. That is class II. A larger class hitch requires a rear subframe attachment. Most of the problems occur with the tongue weight being exceeded, and pulling down on the rear suspension. Few people think of the other problem, towing something => the Volvo, especially while trying to stop.

My brother was moving from Ohio to Florida, then his wife and 2 kids climbed into the Corvair with the VW attached to the rear(loaded with suitcases, etc.). He encountered his first problem going downhill into Knoxville on I-75, the brakes! There was no panic stopping, just very slow slow deceleration and very white knuckles.
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Keeping it running is better than buying new