Swap the ballast from drivers to passengers and passengers to drivers and see if the problem follows the the ballast or stays on the passenger side. I had the same problem you did with the light turning on for a second flickering then shutting off. My ballast was bad and had it replaced under warranty from ddm. If it stays on the passenger side you might just need a relay harness.
As for eagle eyes not taking h11 like it says on the housing it's because they use the aftermarket housing that resembles our stock one, just projectors were stuck in and they never changed the wording.
Mods: GT-R exhaust, CRABs O3 w/FPU, 35% tint, 5000K HID lows/fogs, upper/lower recessed grilles, Racingline strut bar, concept darts, white LEDs everywhere