Yes! You can install a brake controller on the truck. If you intend to wire the truck for the trailer, you will need the 7 way receptacle on the truck and a cord with a matching plug on the trailer. You will need the following circuits:
1 wire for the tail/ marker lights
1 wire for left turn/brake lights
1 wire for right turn/brake lights
1 wire for brakes
1 heavy wire, #10 for charging the battery in the trailer from the truck, this is optional.
1 #10 wire for ground
1 wire for accessories, one example might be backup lights. Again optional.
The problem with your running/marker lights could be corrosion in the fixtures, in both the bulb base and the ground circuit and/or bad bulbs. Once you have the tail lights working go around and wiggle the bulbs in the sockets of the marker lights, check for broken filaments in the bulbs, clean and tighten the ground connections on each fixture. Clean the bulb sockets and the bulb bases if the bulbs appear to be OK. If you get one marker light to work, they shoul all work, unless you have a wiring problem inside the wall of the trailer or a the J box.