How do I “see” the barrel at the insertion point? Am I looking at the target and feeling the lead? Or am I seeing the bird-barrel relationship?
First, lets define “insertion point.” This is the precise point along the target line at which you insert your muzzle.
Personally, I neither plan for nor think about an insertion point unless it is different from the hold point on a given target, such as in the case of a crossing target. For a crosser, you either insert to the target to execute a pull-away technique or insert to the lead if you are using sustained lead as your technique of choice. You should “landmark” your insertion point by picking out a terrain feature to mark it, just as you should your breakpoint, hold point and visual pickup point.
To answer your question directly, lead is “felt” not measured. 100% of your acute visual focus should be on the target through shot execution. Consciously verifying that the muzzle is at the insertion point or seeing bird-barrel relationship necessitates a softening of your acute focus on the target. For a crossing target, plan an insertion point between the hold point and the breakpoint. As the target emerges from the trap and you begin your move from the hold point toward your breakpoint, you feel your shotgun meeting the target at your preplanned insertion point. For a pull-away, you insert to the target, then gently accelerate away from the target along the target line. For sustained lead, you insert to the lead, “working” the target for a fraction of a second, allowing your subconscious to register the correct lead and adjust if necessary.
Successful shotgunning is all about “feeding the brain” by acutely focusing on the target, “feeling the point” of the shotgun at the insertion point and the breakpoint and executing the shot with complete trust that your subconscious will put the gun in the right place to kill the target.