So, I had a little time to pull the bumper and look around a little more.
To summarize, there are two components causing unacceptable headlight shaking while driving. The first is that the whole assembly is permitted to bounce and oscillate. Thumping the top with the ball of your joint causes a "boing" of the entire light assembly. This bouncing them allows any looseness inside the light assembly to go crazy. My driver's side lamp has some loose components inside which bounce around more than the passenger side, though both light assemblies bounce.
With things apart, I'm able to get an idea of what the problem is, and some of it may be design-related. Or, the PO (or service agent) has incorrectly reassembled the entire area after some sort of repair.
The lights are mounted into the body as two pieces. Using RealOEM as a picture reference:
There is the headlight
which mounts atop/within the headlight arm/holder
which runs along the bottom of the light itself.
Here's the fun part - the attachment points.
The headlight itself fastens to the body with two screws on the top. These are visible when you look down at the lights when opening the hood.
The headlight arm fastens to the body with two screws from the front which is hidden under the bumper near the kidney grills. There is a third screw inserted in the rear of the arm from the wheel well near where the bumper skin meets the fender. There is on screw which attachs the headlight to the arm from the side, near where the signal light is integrated into the headlight assembly.
That's it! The headlight fastens to the body with two screws from the top and then another screw which fastens to the arm. The arm is supported from the sides and not the top OR the bottom. There is no bottom support for EITHER the headlight or the arm. If I push lightly on the top of the headlight, it pretty easily deflects downward and will push down on the bumper skin at the same time. Tap it and it goes "boing" due to lack of support from the bottom.
Now, I believe the TSB about headlight shaking only applies to the coupe and the cabriolet. The sedan is in need of a retrofit here IMO. My dad's F10 doesn't have any flex or vibration in the same way my E90 does. I've looked at RealOEM and I don't think pieces were forgotten on my individual car during some repair. If this description doesn't sound accurate to anyone out there, please speak up! I see holes and places that other supports could be attached but there's nothing there.
If I could fix the "boing" of the whole light assembly, I bet that the internal vibrations inside of the light would be few enough that it wouldn't cause me any problems.
The other thing I noticed, is that my headlights contain part numbers that RealOEM has never heard of. The left side is 63-11-6-942-735.
Sorry these are just phone pics, showing my "unlisted" part number and the fact that there are no supports under the light or arm from the front or side.
Note also that parts 11 and 12 look like extra supports and neither is listed for my E90:click for RealOEM