Once I 'get in the grove', I find I shoot better groups during timed-fire strings at about 1-2 second intervals, at least when shooting a Bullseye course with a one-hand grip.
It just seems to be a more natural rhythm, and trying to hold and 'improve' my aim over a longer period tends to result in a greater point of aim wobble.
In the 'slow-fire' segments, I'd better have taken the shot within 5-seconds, otherwise I find it best to lower the gun and start over for the shot.
But this is just me, though a couple other guys at the club have reported better results with more rapid fire as well.
Now that's all relatively slow fire at 50-ft. Shooting bowling pins at 21-ft. is a completely different situation. Five separated targets as fast as you can, starting from a 'low ready' position, and you need to hit them cleanly to get them off the table fast. I'm much better at this than Bullseye at the moment, though not quite as good as the club member who regularly manages it in under 3-seconds. (Or even 2!

I'm happy so far when I'm under 4-sec.

) In this case it really comes down to muscle memory and rhythm. Your muscles don't get the time to fatigue and start readjusting for each target.
Pin-shooting was initially started as an analog for defensive shooting against a human-shaped target, fast and under stress, and I'm not the only club member who seems to hit the target(s) better and more consistently when shooting rapidly like this.