Looking at the factory wiring diagram, this circuit is not properly spec'd. At least in 2015-17 models, the Climate Controlled Seat Module (formerly known as the Dual Climate Seat Module) is connected to a 40A circuit breaker via a 6 gauge wire. That is HUGE so it's evidence of the current draw involved.
This 6 gauge wire is then split into two 12 gauge wires that feed into the module (one for each front seat). But, there is only ONE ground wire going to the module and it is only 12 gauge!
Basic circuit design says the current flowing into a system must equal the current flowing out. So, if a fat 6 gauge wire is needed to feed the heated/cooled seats, the same capacity is also needed going back out.
Dividing up the ground between two pins on the module is not enough. If this were my truck, I would instead run a separate 12 gauge ground wire from the module to the nearest suitable grounding point (maybe behind the right kick panel).
There is an easier way to perform this repair. Rather than cutting all the wires to the damaged plug and splicing them to new wires, instead simply remove the undamaged pins from the old plug (one pin at a time) and transfer them over to the new plug. They can be tricky to extract, but should snap into place easily. Just be sure not to bend the tang on the pins such that they will not snap back in securely.
Once the existing undamaged wires are routed to the new connector, use just two of the wires that came with the connector kit. Cut and splice in a new pin to replace the damaged ground pin, then add an additional pin for a new ground wire next to the existing one. Extend the new ground wire as needed and run it to a suitable grounding point nearby. Be sure to use 12 gauge wire.
