^ Wire gauge cannot be stressed strongly enough. Buying thin cables, or using a cable rated for its maximum load and not its continuous load, is dangerous.
Why: electric brakes are simple resistors, which means even if they're getting 12V and needing 3A (36W) they'll draw that (per wheel), but if by the time the voltage gets to the wheel it's only 9V, they'll draw 4A each. On a 4-wheel trailer that increases the load from 12A to 16A, which while it doesn't sound like much, will have a large impact on cable that is rated for 20A continuous.
Proof: A Subaru Forester owner had 4mm wire installed in his vehicle. Upon braking while towing, the wire started heating up, increasing its internal resistance, causing the current draw to rise even further. The wire melted through its insulator and made contact with the vehicle body and caught fire.
The gauge of brake wire is one area you do not want to consider saving money - use 6mm or better. And that thermal auto-reset fuse - absolutely vital.