It sounds as though the module was incorrectly installed. I'd be tempted to have an auto electrician take a look.
Some years back, I made a DRL system for my '68 Rover 2000. It switched the headlight low beams on, wired in series, whenever the ignition came on. When the lights were turned on by the dash switch, they went back to being in parallel and my "module" (no solid state electronics, just 12V relays) was by-passed. That was the way the first DRL system on the market, made by Volvo for its European market cars back in the early 1960s, was done.
I'm rather glad the US doesn't have a blanket requirement for DRLs. IMO, if every vehicle has them, their effectiveness is greatly diminished. My RV has them, but my KIA does not.
When GM introduced their system in the early 90'd. I thought it was damn dangerous. On one of my Boeing trips, my rental car was a Chevy Cavalier. I arrived at the destination airport after dark, got in the car and turned the key on. The headlights and panel lights came on full bright, so i assumed everything was on and drove the 25 miles or so to my hotel. A couple of times, drivers passing me flashed their lights. The following morning, in the daylight, I noticed a decal on the instrument panel. it was a clear decal with fairly small, white print on it. It said "The daytime running light system turns on the headlights and panel lights ONLY. After dark, use the lighting switch to turn all lights on." I'd driven that trip with no tail lights! The decal was nearly invisible when the panel lights were on.
Frank and Eileen
No longer RVers or FR owners