I’ve seen all the articles with the emg studies on here and its pretty clear which exercises hit each muscle the most but I feel like there’s more to it.
As mentioned earlier I feel like muscles work synergistically (if that’s a word) and when one grows the others in the chain will follow.
Another question. Does my longer arms have anything to do with it? I have loooong ass arms compared to my height. Its only a few inches from my knee cap to the tips of my fingers
If you just look for tricep growth,you’d be way better doing board presses and close grip presses with bands and reverse bands imo
Overhead presses are “for triceps” the way barbell rows are “for biceps.” The basic movement, performed properly, doesn’t hit those muscles as prime movers but definitely does involve them in the lift.
There are variations of the lift that can involve those smaller bodyparts more (reverse-grip rows, for example, or top-half presses for tris.
“Enough” requires context, like knowing the frequency/exercises/volume you’re doing for chest, shoulders, and arms. Some coaches do believe that going hard on presses is all you need for tris, yes. For maximum size though, I say you’re going to want to include at least some direct/isolation work.
Definitely could. Lee Boyce, who’s 6’4", has a few articles about how that changes things. Truth for Tall Lifters is one of them.
Im not bodybuilder, but i believe that heavy compound movements + enough food will give you bigger triceps, and not only triceps 
I have 20inch arms, most of my lifting “career” i did not any triceps/biceps direct/isolation work, but my bench is over 400lbs and strict OHP close to 300lbs, so you could have big arms using compound movements only.
Recently I added to my routine - JM press, this is great exercise to build strength and mass around the elbow, you can go really heavy, load a lot more weight than skull crusher etc. BUT, JM press can really fucked your elbows if you have small arms (ROM is too big for elbows, with big arms forearm touch biceps a lot sooner)
And if somebody have triceps/elbows problems i really recommend ~100rep band pushdowns, its really good way to get blood flowing, and improve triceps/elbows recovery