Understand and some thoughts that may/may not be practical. With a meter, one can likey find which is which on the existing wire by testing that plug while connected to the RV. But then we likely need to have some info from the Brake Buddy folks to tell us which we want where when we connect them? As a first step if we are left to guess, it is "normal" to have the power on the less exposed part of any plug left exposed.
If you have the inner metal part less exposed than the outer, that often means the battery is the inner and the outer, far more exposed, part will be the ground! This is somewhat a guess that might get you into trouble on blowing a fuse if the guess is wrong!
I might suggest just replaing the plug on the existing cord to one that would meet the brake unit but that means KNOWING how to wire the new plug to make them match!
Reversed and plugging is almost sure to blow a fuse somewhere, so I might first want to find that fuse before guessing! Not wanting to blow a fuse that might kill some vital item like brake lights until I know I can recover from my mistakes!