Its chiming like it would if the seatbelt is not on
You can try this manual process to turn off the chime completely. I did it in my father in law's 2012.
https://itstillruns.com/disable-belt-alarm-dodge-ram-7379517.html
Step 1
Sit in the driver's seat and shut all the doors.
Step 2
Put the key into the ignition and fasten your safety belt. Turn the vehicle to the "on" position, but don't start the engine. Wait for the safety belt light to turn off on the instrument panel.
Step 3
Fasten and unfasten your safety belt three times within one minute of turning the vehicle to the "on" position. Then fasten the seat belt one last time.
Turn the key to the "lock" position. You should hear the bell chime one time. This is an indication that the Ram's BeltAlert system has been turned off
As far far fixing the wiring, I'm not sure but
@Mpgrimm2 may know and/or can sell you a harness to correct the issue.
Sent from my HTC U11 using Tapatalk