When to get in line for Vatican reservation

First, there are two lines. Those who have reserved tickets and those who do not. The long line on your left that wraps around the wall is the non-reserved ticket line. Avoid this line. Walk to the right-hand side of this line. Keep walking past those poor souls stuck along the wall. You will come to a metal rail/gate structure. There will be a man wearing a suit coat who will ask if you have reserved tickets. (He is security, not a solicitor.). Say - Yes! You will then immediately walk through the metal rail (cattle shoot) to get on the premises. Then, just go inside and present your tickets to the desk clerk.
There is little to no line for reserved tickets to get into the building.
Things to allow. It can be a bit disorienting your first time to the Vatican. Allow extra time to orient yourself. As you approach St. Peter's square - go to your right and stay outside the square (Bernini building extension "arms" or loggia) to find the Vatican museum. Keep walking to your right around the outside. (North side of Vatican complex.)
Museum is PACKED! Bring the smallest bag you can or leave your bag at the hotel. Checking a bag is problematic. Nearly impossible to retrieve. The visitors herd through in a single direction. A single bottle of water is good to have. No other snacks or drinks allowed.
Once you have reached the Sistine Chapel and are done with it - go out the back of the Sistine Chapel. (This will save you from a 1 hour security line.)
No reentry into the museum at this point. You can now go do the duomo stair climb to get a great view of Rome. Or, you can go inside St. Peter Basilica - or, both!

The answer to your question depends who is standing at the rail/gate and scanning vouchers. I usually walk up the the individual at the time printed on my voucher. I tried five minutes earlier once and was told to wait--fair enough.

Once you have reached the Sistine Chapel and are done with it - go out
the back of the Sistine Chapel. (This will save you from a 1 hour
security line.)

This exit is reserved for tours. While reports of independent visitors getting through are common, it's not a for-sure and some folks have been turned away. It's up to whim of the guards on duty how close they want to check for tour badges.

The exit is worth a polite try. My family and I had no problem leaving through the Sistine back exit. I think security is more interested in visitors trying to enter the Sistine through the exit. (Some tour groups use the "exit" as an entrance into the Sistine chapel.) They didn't seem the least concerned about folks leaving.

Thanks everyone :)

Picky detail. The exit on the back (opposite the altar side) of the Sistine Chapel is a corridor that leads you out of the building. You will be very close to the Dome Climb entrance, if interested.