One of the things that happens in real target shooting, and presumably it can happen in combat too, though it would be under considerably more stress, is a shooter knows he's off target. His breathing is wrong, he feels a sneeze coming, he sees the target jink, or he's otherwise pointing at air.
I always thought that this would be a natural use of the Precision Aiming technique, which is covered in GURPS Tactical Shooting (p. 26-27).
In fact, there would be an interesting way to adjudicate aiming in general, which will add die rolls, but perhaps make a trade-off in narrative fun. We'll see. Consider this somewhat stream of consiousness - so it may wind up all a bad dream.
The way I shoot, you line up your sights on the target, and when you're where you want to be, you squeeze the trigger. The key being "where you want to be." There's no set time for this. Sometimes you're right on and it happens quickly, and sometimes you're not, and you keep aiming. Sometimes, as you start to pull the trigger (especially for single shots), you know you're off, and you relax and don't shoot.
Maybe what you need to do is something like this:
All of this assumes you can see the target.
When you Aim, go ahead and roll some dice. Maybe you always use the Precision Aiming technique (but I don't think so), but I think it's just a straight-up DX-based skill roll. If you succeed in your roll, you get +1 Acc. If you succeed by a bunch, you can get even more, up to the Acc of the gun.
If you want to shoot go ahead. If you hit, great, you shot, you hit, fine.Maybe it's actually this roll, the aiming roll, that you have to trade off in order to get the Prediction Shot bonus that penalizes your foe's Dodge score.
So, what if you fail? Maybe you can make a Precision Aiming roll, and if you succeed, you don't fire. Your margin of success might tell you how much of your Acc bonus you retain.
That way, it's not "I will fire every three seconds," which is basically how it works right now. Sometimes, you might get a very rapid sight picture. Sometimes, you have to work at it.