I've had a problem with my passenger side halo. It wasn't quite like yours. Mine just stopped working altogether. I finally changed out the ballast today, and it now works!
I got my ballast from AAC. Here's the tricky part. I could never get the ballast out of the headlight assembly. I did eventually take off the front fascia and the headlight.
So, I got a little lucky, and I was able to see two white wires that connected to the halos. They have a white connector on the end. I snagged them and taped them to the assembly, so I wouldn't lose them.
While I was fiddling around with the ballast, I noticed 2 more wires - one pink, one white. The connection on the end matched the connection to the 2 white wires. I ended up grabbing them with some needle-nose and pulling them off the fried ballast (which was still stuck inside the assembly). Then, I connected the 2 connectors and snaked out the pink and white wires outside the assembly. Next, I just wired together the pink and white wires with the Oracle ballast, and it worked!!
At least now, my ballast is outside my assembly, so if that goes bad, it should be an easy fix.
Let me know if you have any questions. I wasn't too sure how to fix this either and kind of got lucky.