You're supposed to keep both eyes open when shooting. Having said that, how many don't?
One eye should be seeing the red dot, and the other should be on the target. The brain will place the red dot on the target in the right spot.
There should really be no focusing on either target or red dot required.
However, since most close one eye or train themselves to focus on the front sight, we have to look at the mechanics. A red dot doesn't require front/rear sight alignment. So, focusing on the dot doesn't accomplish the same thing.
Focusing on the target in a fight is much more important than where the dot is. By the time the dot registers in your mind and you get it on target, it's too late unless you're not exposed.
I like to practice keeping both eyes open with the red dot. Even if you're cross-eye dominant, your brain still sees the dot in the correct spot.
Just my 2 cents. Practice, practice, practice.