I think the solution, especially for stop/start cars is to follow the 'hybrid' instructions which should keep the lights illuminated even when there is little or no alternator output, this is also the method hinted at in the troubleshooting by connecting to a particular fuse or Acc power feed.
The Phillips DRL controller is intelligent in order to simplify wiring (up to a point) and in theory can detect when the car is running and switch the DRLs on, trouble is it seems to think this is not all the time such as when the voltage at the battery drops close to it's resting state. I think rather than follow the instructions by directly connecting to the battery, you should connect to an ignition switched supply instead and set them up to ignore the battery voltage and just switch on directly when they receive power (and off when the sidelight sense wire sees voltage).
The blue wire sounds like an battery sense override wire, so connecting this to an IG1 switched supply should help.
The original answers are directed to a MK1/GD owner but the same theory applies to the Mk2/GE. This could be done without an intelligent controller and just a relay instead so the sidelight sense wire cuts the feed to the DRLs.
From a VW forum linked above:
I bench tested my kit before install because some posters were concerned about current draw or flattening batteries. The DRLs power on at about 13.5 volts and are off at 12 volts. If the lamps are forced on at 12V a pair take 0.9 A (12W). At 14.5 volts (alternator charging) current draw is 0.7A (10W). When the DRLs are 'off' the control unit draw is 3mA. This small current should not significantly add to battery drain.
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TG