Lets say there was a planet that is 1/10 light year away (for a close mission), given the speed of light is 186,000 miles/sec. The planet is stationary, neither moving farther nor closer from the launch point of a vehicle heading to investigate it.
Given the speed of the vehicle as a constant, the vehicle travels to the star with an estimated arrival date derived from the vehicles speed in relation to the speed of light.
If the vehicle arrives there not on its estimated date, but the actual arrival date, this would prove the speed of light is no longer its current value, but a totally different number.
But also if it can be proven lightspeed is infact a varible, this would totally throw current measurements out the window as the possible distance can not be accurately measured between two bodies.