The problems you are describing are typically associated with a poor ground connection, but it could also be the result of a faulty converter box if you are using a plug-in style wiring harness like the Curt T-Connector Wiring Harness, # C55334, that you referenced.
If the wiring harness was working in the past and the problem just started, then the converter box could have shorted out, which would cause a variety of different issues. If this is the case, then I recommend replacing the... view full answer...