I don't think the integrated trailer brake controller, by itself, can activate a single brake, but the stability assist or stability control (now a Federal mandate) certainly can, that's they way these systems work.
But if you are burning up a single brake, that's not ESA or a brake controller, as those are instantaneous and intermittent. What you have is a dragging brake, a mechanical, and maintenance problem. It can be in the caliper or the hoses. Mine was on a left rear brake, and the problem was corrosion in the caliper, fixable with a superior replacement. Just as often, the problem is a collapsed brake line (hose) that prevents or delays retraction of the piston in the caliper.
Let a brake shop figure it out. Or replace the caliper and the hose.
