2015 Mitsubishi ASX LED DRL's

[MadMax]

maybe its the issue of wattage (i.e. more watts less current)? try to get those generic control boxes of ebay, most will come with voltage sensing relay anyhow

More likely to be a votage problem that wattage, LEDs don't draw much current.
Any idea what voltage these run on?
The control box may just be a DC to DC step up transformer, if so, just wiring the 12V input of this device to any source that comes on with ignition should do the job.