I presume you have downloaded the 2006 KJ Service Manual here which has the wiring diagrams?
http://www.colorado4wheel.com/manuals/Jeep/KJI however cannot make sense of the page 8W-50-2 which is for the relevant circuitry....and I am a retired Electrical Engineer! This is not too unusual though as there are lots of errors in the wiring diagrams
Have you swapped out the High Beam and Daylight Running Relays?
I am not too familiar with Daylight Running lights which I assume are only applicable in Canada.
I know it involves fitting a robust relay in the top-left slot on the fuse panel (Junction Block). Does it also require any programming in the BCM? The diagram 8W-50-2 shows the BCM as well as the Multifunction switch are involved in energizing the High Beam Relay. So maybe the BCM programming is wrong or the Multifunction switch may be faulty.
With your meter set to DC volts pull out the High Beam relay and place the leads into female pins 85 and 86. With the headlight High Beam switched ON you expect to see a constant DC voltage of about 12 volts...if the meter reading drastically fluctuates let me know. Now put the meter on DC volts first then AC volts with only Daylight Running Lights On....you should read nothing unless you have a rapidly fluctuating voltage creating a form of AC voltage.
I will read up on how this system is supposed to work and will check up on what BCM functions can be programmed.