I just went ahead and replaced the whole unit, the vent selector on the far right was completely fried, where the fan speed selector actually worked fine. The half moon internal mold of the dial knob itself was broken being that it’s 20 years old and made of plastic.
View attachment 405272
View attachment 405273
For anyone who has a similar issue, here is where I got the entire new unit.
HVAC Climate Control Panel for Jeep Wrangler TJ 1999-2004 Heater Selector Control Switch, Climate Heater Panel Air Conditioning Control Unit, HS-373 55037473AB
https://www.amazon.com/dp/B083WD1JBC/?tag=wranglerorg-20
If you need to replace the far right adapter from melting, I bought the mopar repair kit. I explored the option of using female adapters or soldering but I didn’t want to run the risk of shorting considering there is not much space between the prongs. I also was not able to find a cheaper alternative :/
Mopar - OEM Connector Repair Kit - 68080536aa
https://www.amazon.com/dp/B007NNI8TM/?tag=wranglerorg-20