It's almost a 2 part question. You want a more active triceps (implying a better mind-muscle connection and development) and a stronger triceps (implying better recruitment).
While I love top half presses either overhead, incline, decline or flat and they ARE great triceps strength movements. I feel that if your triceps is lagging they might not be the best solution, especially not if your mind-muscle connection with the triceps is bad.
I see 2 specific issues with these movements in your case:
- If your mind-muscle connection with your triceps is bad, and if they are your weakest pressing muscle, any pressing exercise will tend to shift the tension to other muscle groups (chest or shoulders). YES the reduced range of motion puts more stress on the triceps but the other pressing muscles can still compensate, especially the deltoids.
I find that top half presses are very effective to build triceps strength IF YOU ARE ALREADY GOOD AT USING THEM.
I'll use myself as an example. Triceps use to be one of my better muscles. Top half press worked amazingly well and were a huge part of taking my bench press up to 445 at the time.
When I began training on gymnastic rings a few years ago I trained something in my elbow and ever since that happened I lost some contraction capacity in my right triceps. I've done top half press since then and they didn't help at all. I could feel all the stress being take up by my right shoulder and the left side followed along, which made the movement ineffective as a triceps builder for me.
If you have a hard time utilizing your triceps to the fullest in heavy pressing movement or if your mind-muscle connection with the triceps isn't that good, the top half press will not help you much.
- I now tend to try to avoid adding more heavy exercises to a program already based on tons of heavy movements. If you are doing several heavy pressing exercises already, adding one more, even if it's a partial ROM, could lead to stagnation or even regression via neural fatigue. Or it could eventually lead to soft tissue injuries. Unless you are genetically designed for heavy work (super thick joints for example) adding more and more heavy work will rarely be an effective solution.
Now if the partial presses replace another heavy pressing exercise that's fine. But you can't simply add one more heavy lift to a program already loaded with them.
I don't know what you do in your program at the moment. But the solution could be as simple as adding isolation work for the triceps. Make them bigger and improve your capacity to contract them and they will gradually become more and more integrated in your heavy lifts.