Has the running lights on the TM ever worked with the
NEW TV? Did the running lights on the TM work with the old TV the last time you had it hooked up?
Can you use a volt meter or test light to test the 7 pin connection on the TV?
see link for 7 pin wiring.
http://www.hopkinstowingsolutions.co...ng-guides.html
"if one of the many yellow running lights has a bad bulb, if that effects the entire circuit?" They are not wired like Christmas tree lights. One bulb should not effect the others.