I have new drywall which I prepared with 2 coats of primer. The semi-gloss paint finish sheen is uneven on the wall. I went back over certain areas with another coat of paint. Better, but not perfect. Should I have put a third coat of primer on the wall-especially where there was no mud? Is the solution a one-stroke brush/roller stroke from top to bottom? I am trying to achieve a smooth finish on the walls. The wall has lots of sunlight (big windows, south & west light).
Lots of moving pieces here. I am assuming though that you are using the exact same paint.
First your two coats of primer might not be mine. Meaning a "coat" is subjectively what you think it is.
My definition of a coat is hitting the entire wall with what I think is enough paint to cover it completely as quickly as possible. In my head I know that if I go up to the wall with a microscope - or it gets hit with the right angle of morning sun... well there are probably quite a lot specs missing. So a coat to me is wall looks painted from 30 feet.
That being said. On fresh drywall... I do "two" coats the first time through a wall. Then about 2 hours later I give it a really hefty third coat... Which you may think is a fourth coat.
Now if I am doing a light colored eggshell I can go lighter on the 3rd coat. With a semi-gloss - it is heavy primer then a good three coats of paint.
The unevenness is either from you having areas not primed enough so that your coats of paints had to initially prime the wall... or you simply did not put enough semi-gloss on the wall. There really isn't a perfect technique for doing this right. It is whatever you can do to stay roughly even - but for sure you should be using a good low nap roller, not a brush (unless you want a unique uneven look, or you are a budding artist).
Even after I overprime a wall I am hitting it with 3 coats if it has a lot of sunlight hitting it. The sheen is duller in areas because like I said before those other areas were not primed as good or you missed it a bit on the first couple coats. You don't need to dwell on that. You need to keep adding very light (and even) coats until you are happy - nothing else you can do.
Note: I do not think this is your issue but worth the mention. I don't trust the "sheen level" on paint until it cures. When you add new egg shell to old it for sure looks shinier - like not matching shinier. 3-4 weeks later hard to see the new paint.