it is really quite simple.
Just run the wires from your TV.
pic your colors who cares, it doesn't matter just don't get confused
1- ground
2- 12V
3- left turn
4- right turn
5- brake
6- reverse
7- running lights or park lights
find all of these wires in your TV. Tap into them and put them into a 7 pole connector then continue them back to your trailer.
And NO , those converters will not work in reverse. they are to reduce from 5 to4, they will not increase from 4-5.
NOW,if it were me??? I would just go get some standard lamps for the trailer and install them in 4minutes
good luck