Wow that’s a perfect example of one thing leads to another.
took a bit of troubleshooting simply because my HID kit on there is my own aftermarket creation and the relay "buzzing" was a 1st. I had no idea the running lights were out initially.
I started troubleshooting at the relay and testing each part from the relay back and then I found it was creating high resistance when the truck was in drive (drl's) kicking on, which in my case turns the HID's on appearing to make the voltage drop to around 6.5v. but worked fine if the headlight switch was turned on.....
i knew the high load and low voltage was why the relay was buzzing, but no matter what I tried it didn't fix it.
so I was scratching my heading and telling my wife this makes no sense lol.
that's when I started swapping relays and replaced a relay in the wrong slot unwittingly, those all seemed good and nothing changed so I started checking fuses and found the blown running light fuse, but the running lights didn't work after replacing the fuse because the relay was not where it should be so I was really going WTF?
so I got the manual out and starting looking at the fuse box and saw my dumb butt had moved the relay to a "upfitter" slot, put the relay back where it belonged and everything worked again. ugh
at one point I thought maybe I had pinched a wire or something when I put the trim panel back on the rear hatch because there is crap ton of wires in the hatch but it is not "easy" to remove the trim cover and I had already broke one clip so I really didn't want to go down that rabbit hole, none of the wires had anything to do with the taillights except the hatch switch. glad I found my problem under the hood