I think at this point I’m just going to let it back bud and grow a bit and tell me which direction to go. How many times can/should these be pruned in a season? Last year it basically grew all spring summer and fall and flushed out every time I cut it back, maybe three or four times. Is that too much?
Privet can be trimmed many times through the grow season but that may not be the best course of action at this stage of development.
Most of those branches need thickening. That happens faster when they are allowed to grow longer with lots of leaves. Takes many years if you keep cutting off new leaves.
Don't worry about branches getting too long on privet at this stage of life. They respond so well to cutting back. Allowing the branches to grow long then cut back hard will usually result in a mass of new shoots which will build ramification.
I generally let young branches grow for an entire season (wire for direction if required but watch that wires don't mark the bark) then cut right back to 1 or 2 nodes. Allow the new shoots to grow for half a season (wire for direction if required) then cut them all back to 1 or 2 nodes and allow the new shoots to grow the rest of the year. In the following year trim whenever new shoots grow to 4-6 nodes.
If everything has gone according to plan the branches will now be thicker and have many side shoots and look like real branches instead of sticks with a few leaves.
I have found that you need to prune way harder in initial stages at plants only ever grow outward so during development your trees will occasionally look overgrown and sometimes like bare sticks. Knowing when to allow each takes some time to learn.