Bolding mine. How is the gap growing, if the cars are accelerating at exactly the same rate?
The one second difference exists because they started at different times (reaction) and/or the lead car was initially accelerating faster.
I think the disconnect here is how we are defining the initial setup. If we think about an extreme case, consider two cars running the half mile. One car takes off a few seconds early and the second car doesn't launch until the first car reaches the 1/8 mile mark. At that point, the second car leaving late can out-accelerate the first car for a while with the gap between the two cars still increasing: because the first car is already up to speed (say 90 MPH) and is gaining ground on the second car. At the point when the late car catches the speed of the first car and finally starts to decrease the gap, yes, it has been out-accelerating the lead car for quite a while.
My setup was different, as in the video. One car dropped behind but they were close enough that there were about 3 seconds where the trailing car neither gained nor lost ground. During that 3 seconds, both cars had the same speed and acceleration: during that 3 second window (looks like about 80-115 MPH), that has been established since the only way to change the gap after that 3 second dead heat is for one car to out-accelerate the other. We were talking about EVs losing rolling races at higher speed so in this case, in an 80-115 MPH rolling race, both cars would be dead even. After about 115 MPH, the ICE would pull away. And keep in mind, in the video example I posted, the ICE is rated for more than 100 HP more than the EV.
Mike