The tail lights
, stop lights, exterior marker lights are not connected to the trailer battery but are extensions of the lights in your tow vehicle.
As has been pointed out in a different thread, there is a potential for serious safety problems with incorrect or poor wiring. It took me a long time to get to the point where I felt comfortable with electrical wiring, but after 50+ years of working with it some things have become intuitive to the point that I feel a certain confidence doing these things. My point is that it may be the better part of valor to get help from someone who has plenty of experience in this.
When working with trailer wiring on a used (or new) trailer I would NOT rely on color coding, as a rule. Rather rely on a multimeter or some similar device which can tell you about polarity, continuity, voltage, etc.
As Byron K. points out, use wire that is meant for automotive use. A trailer moves and shakes, and the resulting friction and rubbing demands strong insulation and good anchoring. Proper fusing, even if you have to resort to in-line fusing, is your greatest protection against disasters.
About the Newmark: the picture shows what you find when you take the case apart. Most of that stuff goes, so if my memory serves, the grafted on new converter ends up using greatly simplified wiring. I cannot give you a schematic, but someone familiar with trailer wiring should find it a piece of cake.
No offense meant, but for your safety I would recommend getting an "electrically experienced" person to help you.
Another recommendation: my preference is for soldered wiring connections, not just crimped ones or wire nuts (that vibration thing again) followed by plastic electrical tape and heat shrink tubing. I have spent a few minutes in our Burro
on a terrible gravel road and the jostling was incredible.
Thomas: Unfortunately I cannot give you the specifics of the wiring done many moons ago, but in the picture you see of the new unit mounted I left most of the rear enclosure off. The new unit fits easily into the box, so when you look at it with the panels back in place you may not notice anything has changed.