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Although I know you tried the aluminum foil shielding, I did forget to mention to make sure that the foil is grounded. This is an important point. So if the foil wasn't grounded, I would recommend doing that test over again. Wrap foil around all the lines from the ballast and even around the ballast. You could even bring it over the back of the head light reflectors. If radiated EMI emissions from the ignitor is the cause, a grounded metal shield will definitely attenuate the emission. Also, since you have the foil roll out, shield the amp and its wires' too, and ground it to the chassis ground.
Another engineer at my work suggested separating the ballast and amp grounds as far apart as possible in case transient ignition emission is being conducted by the amp's ground. Personally, I doubt it, but it is worth trying just to eliminate the possiblity.
Solving EMI problems is a step by step process, but ultimately I think you will solve it. (I remember a few years ago we had one light source that took 2 engineers a month to make pass EMI, so sometimes it can take awhile)
One other thing, try to make the wires between the lamp and the ignitor as short as possible in your installation. My experience is the less wiring running around, the better. I'm under the impression that the ignitor and ballast are in the same housing. If not, move the ignitor right next to the lamp.
If the foil is touching bare body metal, it is probably grounded, but maybe not well. There isn't much grounded bare metal in that headlight well, so I would take some bare copper wire, attach it to your normal grounding point, and wrap the other end of it 4 or 5 turns around the foil sheathing.
Ever since the HID install. I have a CDA9813 Alpine deck and an old Alpine 3525 amp. The pop is not too loud. The stereo shop did have to put on an engine noise filter near my amp.
With the new head unit in mine and the amp under the passenger seat there was no pop, but I didn't remount the amp in the trunk so I'm not sure about that location and impact.
I had reached the end of my rope and had decided that if the Alpine installation didn't fix it, it was going to stay as is. The popping didn't occur every time and was only very brief.
Good luck and let me know what you do and if you resolve it.
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