But in this case, I wasn't thinking airwave, but direct connection through the same wiring route. I'm not much for electrical circuitry, so I'm just taking wild stabs in the air. But the fact that simply pulling apart the connector that goes from the headlamp switch to the ballast makes it work tells me that it's definitely the ballast causing interference somehow.
Interference not as in electrical interference over the airwaves (that wouldn't keep the little led from blinking) but interference as in its interfering with it working right; ok

Take a look at the yellow and white wires to the headlight. One for high beam and one for low beam. Black wire to the original headlight plug(s) is the ground.
A ground connection will go to one side of each ballast.
The low beam feed supplies one ballast.
The high beam feed supplies the other.
We'd talked about all that before.
Now take a look and see where you're tapping in to the high beam wire. Is it tapped in the harness somewhere or are you plugging directly in to the headlight socket? If plugging directly in to the headlight socket are you sure you have the polarity correct?
I'll be up another hour or so. Give a call if you want to.