I'd go for replacing the converter box and all wiring rearward to the hitch area. Even though you may never tow, it's not an expensive fix. I'm a bit confused why your vehicle would have both 4 and 7 pin connectors at all....but then again I'm not a regular tow guy either.

If the wiring for either is not stock and added on by the PO, your best bet is to tear it all out and put in new.

These aftermarket converters are a big source of problems when they get old.

This option looks a little simpler if you just need the converter. For those that have done this, does it look like a fix for just a bad converter?

Amazon.com

Update: I used this part successfully. Just a little wire cutting and splicing. Tips: The car side of my wires were all green/striped - only 4. Use the 5 wire side to connect to the car side - the fifth wire is ground. Since I installed without a trailer attached, I used a multi-meter to determine what wire was blinker, brake, etc. And then connected per the color guide of the converter. On the trailer side of the converter (4-wire), I just matched the colored wires (they were the same colors on my '99 LTD). Last tip. On the side panel (driver side) that needed to be removed (actually just pried open) there is a plastic latch in the middle of the panel connected to the body. This latch needs to be lifted a bit to remove/pry the panel. Worked perfectly!