Hello, I've been wondering for a while why runs start the frame that 400 appears on the timer. Why doesn't the run start when the player gains control of Mario, the frame before the timer appears?

Because Mario actually doesn't move on the 1st frame. Any input you do a frame before 400 appears will make Mario move on the frame 400 appears

FCEUX has a frame delay between when you push an input and when you see the result of that input on the screen. (Have you noticed that if you push jump and then frame advance, you don't see Mario jump on the next frame, but rather on the frame after that?)

So the first frame of control is in fact the frame that the "400" appears. It only looks like you gain control a frame earlier ($E set to 8 ) because of that delay.