Well if you're pulling a trailer with good lights and your running lights work on the camper then nothing to worry about for the time being.
you still didn't say if the new plug is on the old wires in place of the old plug or if it's totally new wiring connected to ?
Sporadic brake light means a short somewhere probably. Are you sure it's only working sometimes?
The turn signal/ brake light issue sounds like they tapped new wires into the individual tail lights incorrectly.
Yes it could be as simple as switching a couple wires around but if you're not willing to open up and insect what you have then it will not get fixed.
There are diagrams that show which color/position on the different plugs is for which lighting functions.
Real difficult to trouble shoot elect issues over the Internet without detailed info.