Einstein saw a problem with a physics. He carefully thought about this. He saw that all determinations of time had to do with simultaneous events. But then he inquired into what is meant by 'simultaneous'. It turns out there was a lack of consistency there. He then determined that he must stipulate that light is constant, or else no consistent definition of simultaneous events could be devised. That would be no ability to determine the time of an event. That would be the end of physics!
Einstein does not say that light is constant. He defines that light is constant.
"But Einstein, you say, 'how do you know light is constant?' " He would ask you to prove that it isn't. You would then have to make determinations of time -- which you can't do with defining what simultaneous means, rigorously. (Which you can't do without stipulating that light is constant).
Light, time and space are so fundamentally related, that they cannot meaningfully be separated. Any determination of space and time must include light. Also, there has never been a location without a time, a time without a location. There has never been a determination of space or time without light.
Time and space are related by light. Namely, x^2 + y^2 + z^2 = c^2t^2. This is true for the propagation of a ray of light. How do we know that it's true for all points (x, y, z, t) on the space-time grid? It has to do with our definition of time. Remember: Einstein saw a problem with our definition of time.
Any space time reality/grid must be constructed through light signals. Whether the light is constant or not is immaterial. There is not other way to consistently construct a space-time grid.
We say that two clocks are synchronous if the clock at the remote area is equal to 1/2 * of the following quantity: the total time (as judged by the local clock) to be propagated and reflected back from the remote area.
Light (and therefore it's propagation) plays a decisive role in the determination of time(s).
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