A very good question. In a perfect world it's best to shoot with both eyes open, I was taught to shoot that way by the military. With both eyes open you'll have a better chance of picking up the targets sooner. However, it can present dominance problems to some shooters. This seems to be more prevalent with skeet's crossing shots than with trap targets.
For me the problem occurred intermittently with Skeet's low-three target: While swinging on that long target, just as I was seeing my lead it would seem to take a jump, I'd correct my lead, and inevitability I'd miss. My squad mates would tell me I'd missed by a mile, but to me the lead had looked correct. What happened was my left eye had taken over. In a non-technical analysis, I felt my subconscious got bored tracking that long target and switched eyes as a diversion.
I'm not alone with this condition, other folks I've competed with in Skeet and trap describe the same problem. Having the targets seem to take a jump as they are being tracked is not uncommon. There's a simple solution, place a small spot of tape on the off eye lens of your shooting glasses -- about a half-inch in diameter and positioned so it prevents the off eye from seeing the muzzle. You may have noticed shooters with tape on one lens, now you know why. I tried the tape for several years and it worked successfully.
Another method is to close your off eye as soon as you pick-up the targets and track it with your gun eye only. This requires a conscious effort and you might forget with a problem target. I'm not sure what you do when shooting doubles. Obscuring the off eye is automatic.
Part of competitive shooting is continually fine tuning your technique in an attempt to shoot higher scores. This is especially important as you age and you eyesight and reflexes slowly change. For me it involved moving my hold point out and waiting a little longer before making my initial move on the long crossing targets. Having less time on those crossing targets cured the jumping target and I removed the tape. I guess my subconscious no longer had the time to get bored.