Maybe its like the bullets from the guns of the proposed fighter the SR-71 was based on.
If thats so the photons would stack up in little piles on the end of the headlight until something else interacted with them and pushed/pulled them off one way or the other.
If the headlights were cone shaped could we allow them to pile up inside until there was a hemisphere of photons sticking out?
If we licked it then what flavor of ice cream would they taste like?
The bullets from the plane that shot itself down traveled faster than the plane initially, they were slowed down by friction in the medium in which they traveled (air) while the plane had constant thrust so it did not slow down and ran into its own bullets.
In order for light to behave similarly it would have to be traveling in a medium (Aether) that limited its speed, and then its speed would be constant relative to the medium but not relative to other objects traveling at different speeds or in different directions.