I skimmed through about 1/2 of FMVSS 108 last night and didn't see anything about degrees of visibility for rear lights except something about 45 degrees. There are a lot of references to SAE standards and maybe the 135 degree requirement is there. Reading federal vehicle regulations is almost as bad as reading the tax code!
You have correctly surmised that the angle of visibility requirements are defined in the SAE standards. The SAE requirements are incorporated directly into the federal code by reference (and the state codes must follow the federal codes through a different set of arcane laws).
Here is what I wrote on the topic on the other board, in an argument about whether it is legal to use drop-in replacement LED "bulbs" in an incandescent fixture (it's not):
I refer you to Federal Motor Vehicle Safety Standard 108, also known as 49CFR571.108 (and it's Canadian counterpart, CMVSS 108) which says, in part, that required lamps must conform to certain SAE specifications. For Stop lamps, that would be SAE J586c, and for Turn Signals, SAE J588d.
Both of those reference SAE J573d, "Lamp Bulbs and Sealed Units" which requires the filament of the bulb to be within 0.01" of the position specified by the manufacturer when the lamp was designed. Filament positions are specified in section 220.127.116.11
LED "drop-in" replacements do not meet the specified filament positioning, therefore they do not meet SAE J573d, thus making the installed fixture in violation of SAE J586c or J588d, thus violating 49CFR571.108 making it UNLAWFUL.
I don't know how much clearer I can be on this, and you making blanket statements like "Nor is it prohibited" without, apparently, even a cursory attempt to research the law is irresponsible.
We could debate until the cows come home about whether an aftermarket lamp could conceivably be inserted into a fixture and meet the photometric standards (and, if they could, then a manufacturer could, conceivably, certify the resulting combination of specific fixture and specific LED as compliant). But as the law is written today, it simply is not lawful to do so.
Nor is it lawful to, for example, retrofit an HID lamp envelope into a headlight system designed for an incandescent lamp. That does not stop hundreds of companies from selling retrofit kits (most of which have "off road only" weasel language on the package) -- the presence in the marketplace of these items does not make it legal to use them on the highway.
FMVSS 108 and the SAE standards are actually quite particular about what you can put on a highway-legal motor vehicle.
Anyway, the reason I asked for the code cite is that I know full well that it does not exist. That individual also went on to say that "... brightness [is the] the only important quality of a light bulb ..." which is also incorrect; as you can see from my description, the precise location of the filament is also important and explicitly defined in the law, as is the photometric output of the lamp at various angles.
The law does not contemplate individuals photometrically testing their own lamps. Instead, it relies on manufacturers doing this testing and then certifying that their fixtures meet the SAE requirements. Such compliant fixtures have appropriate markings embossed on the lenses to indicate compliance.
As long as you use DOT-approved fixtures (in accordance with their directions -- for example, if it says that it must be mounted within so many degrees of vertical, then that's the way you have to mount it), equip them with the bulbs for which they were designed, and follow the placement requirements that I linked from the NHTSA earlier in this thread, you are covered. There is no requirement that you use the same fixtures (or number of fixtures) that the OEM coach builder used, or that you do individual testing of your coach to photometric standards. (Of course, the fixtures can not be recessed or otherwise mounted such that part of the vehicle obstructs its visibility from all intended directions.)
Note, BTW, that some fixtures are approved for "combination" use. For example, a single "corner" fixture photometrically tested at 45°, if so listed, may be used as both the rear clearance lamp and rear side marker lamp.
Most of us, I think, find the minimum defined by the standards to be not entirely sufficient. For example, there is no requirement for side-mounted turn signals, yet every major coach builder puts them in. I have them front, center, and rear, mounted just underneath the required side markers/reflectors.
Hope this helps.