DOT probably gonna' go with the FMVSS 571 vehicle safety regs .
Check out FMVSS 571.108 S14.9.3.11.12.2 then just below in table 1-A and in next table 1-b and 1-c it talks about stop light locations.
2 Red....
On the rear, at the same height, symmetrically about the vertical centerline, as far apart as practicable....
Not less than 15 inches, nor more than 72 inches.
I didn't search too hard for a aux single center mounted brake light.
I would drop by your local state troop hdqtrs and ask that question to a certified size and weights officer.