Check out this interactive demonstration, which shows how we would expect light to behave based on non-relativistic experience. Use the slider to pick the train’s speed, and then click start. The flash heading forward would travel faster, getting a “kick” from the train’s motion, while the flash heading backward would travel slower, being “dragged” by the train’s motion. Were this the case—it’s not—notice that the light would reach the front and back ends of the train at the same moment from all perspectives, regardless of the train’s speed.