According to what I read, the ZC1 is a kit to provide trailer light control. An installation guide is here
. It says you can put the control module into "learn" mode to reset in in the case where the outputs are not working as expected. I would try that first.
As "hillbilly3" said, these kinds of symptoms often arise from poor or intermittent grounds. I would check the ground connections on all the connectors (tow vehicle and trailer), and through any umbilical cables that connect the two vehicles. Sometimes you have to pull or twist on the wiring to get an intermittent failure to occur "while you're looking."
Now, the potential interaction with the trailer electric brake controller is a puzzler. The controller takes in a single signal: the brake light signal on the tow vehicle. If a failure occurred such that the bake light signal was on all the time, then the controller would perceive that as a brake application and put out a strong (and perhaps constant) signal on the trailer electric brake controller wire (the "blue" wire) at the tow vehicle hitch connector. In that case, though, the cause of the problem would be in the tow vehicle. In this scenario, you should see the brake lights on the tow vehicle (with the engine on), when no one is pressing the tow vehicle brake pedal.
Could you provide the make and model of your trailer electric brake controller?
Could you tell us what the connections are at the rear of the tow vehicle? The ZC1 uses a 4-flat plug; the trailer electric brake controller uses a ???