Follow through simply means that you intentionally keep doing whatever you were doing at the time you decided to break the shot. The idea is to keep from unconsciously affecting the shot. Without consciously following through, a shooter may actually start to relax before the shot in a target-shooting environment. Or the shooter might stop swinging the shotgun before actually pulling the trigger in a wing-shooting situation.
You said my eyes should not follow the front sight during recoil but I do need to keep track of the front sight.
I'm assuming that you're holding the gun in a normal grip and that it's not a heavy-recoiling magnum revolver or something similar. The front sight should never leave your field of view even if it does move upward during recoil. So you keep track of its general location as it recoils upwards and recovers back onto the target, but you don't need to actually track it with your eyes as it moves. In fact, I don't think many people could actually track it accurately with their eyes even if they tried.
If you CAN actually track it accurately with your eyes as it moves upwards and then recovers back onto target in the fraction of a second that takes, then that's pretty impressive. I don't believe that doing so buys you anything, but I doubt many people have that ability.
If I don't keep my focus on the sight, I must therefore focus on the target (or the next target), at least for a brief moment. In other words, I will have to leave my front sight focus for a moment after the shot breaks, focus on the target (or next target), until my sights are realigned. Then I focus on the front sight again.
Trying to change your focus back and forth between the target and the front sight will slow you down unless you can focus your eyes very rapidly. Maybe even if you can.
Your comments leave me sort of at a loss.
On the one hand, the implication that you can focus on and track the front sight as it moves rapidly in recoil and that you can change your focus from front sight to target and back in the fraction of a second that it takes to transition targets suggests that you have very impressive visual acuity and should be shooting very well if your trigger control is decent.
But the way you're asking the questions and some of your other comments suggest that you're having trouble with the basics.
I don't really know how to reconcile the two. I've started trying to type responses several times but they keep self-destructing because of the way the implications of your comments and questions contradict each other.
Maybe let's start with your basic skill level. If you're transitioning between multiple 8" targets at 10 yards or so, how many shots a second can you fire and still make your hits?