ahhhh proper bend your mind question.
Right, from my wacky interests in question like this, this is my understanding so far.
The speed of light is not constant. Light is an Elcromagnetic wave and like all waves, it depends on what its traveling through, but i assume you mean the speed of light in a vacum, like in space.
Now with a bit of weird Einstein theory, we can say that Time is not constant. Its merely observed from us people going round at stupidly slow speeds comparried to the speed of light in space.
So with Time not being constant, and if you are going round at the speed of light, you would not be able to observe any changes, so in effect time would appear to stop. (The phrase of time slowing down normally reffered to as Time Dialation). The faster an object moves, the slower time passes for the object.
This effect can be messured as the GPS salelites knocking round the Earth have a yearly time correction of 1/1000000 of a second (or there abouts).
If you were at the speed of light with your lights on, then from the stationary observer, the Mass of the Vessel and light would appear at the same time, from the passengers perspective, nothing would be happening atall as time would have appeared to stop, but with no time passing then they would not know.
If you were traveling a a fraction under the speed of light, and you turned your lights on, then from your perspective on the vessel at speed, it would appear that the light was beamed ahead normally, how would you know that time is slowing for you?
From the observer stationary there would be a difference between the light and the mass. but as the mass is not traveling at the speed of light, it doen't really answer your question.