Are they earthed simply by being bolted to the bodywork? If so, one could just not be making good contact with the metal of the car body. You could try running a dedicated earth lead from the DRL to a good earth in the engine bay and see if that cures the problem.
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I have already tried simply swapping over the actual flickering light with a new one and that also flickers, so it's not the bulb housing.
I think you missed the point. What if the new one is also faulty?
Which is why I suggested the simple swap of position of the known good one (i.e. the old one that doesn't flicker) with the position of the old flickering one or new one. Then see if the good one flickers. Flickering of "good one" would point to a harness (wiring problem).
A simple thing, without needing needing to resort to multimeters etc.
FWIW, and following on from SHCMs point about maybe the new being faulty, I have bought quite a lot of LED lights of various fitment styles and the general reliability of them both out the box and over time has been very disappointing
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