In my short experience open connections are more common than shorted wires on trailer brakes after a few years of weather exposure; however either may result in no brakes. Good brake controllers run a small amount of voltage through the circuit and check for proper current flow giving a warning if it’s not there. Instead of spending a lot of time checking through the whole circuit for problems, I suggest just running new wiring from the 7 wire umbilical junction box to the wheels with all new splices at the box and wheels. One 10 ga. brake wire is the minimum for 4 wheels. I prefer to use 2 12 gauge wires, one to each axle which results in less voltage drop (and more brake action) to the wheels. I run one to each axle so if I lose one, I at least have the other axle’s brakes. My son was having the problem of no/low brakes on his trailer. After running the new wires, he can’t believe how much he has to turn down his controller to keep the wheels from locking up.