This is such a great discussion!
I think there are several layers of "stage presence" that become relevant depending on where you are in your career and what kind of performance situation you're entering. Most young players are dealing with basic presence, and as you grow you really start to see stage presence as something that is as much a part of the show as the music itself. I'm fortunate with Presidio Brass to be able to get a lot of feedback from audiences. One thing Presidio is known for is the interaction with the audience, and the energy that makes it's way from the stage to the audience. Presidio video records and reviews every show we play (Well, some venues forbid recording even for personal review). One thing we implement as an ensemble when we're reviewing a show is to focus our attention on members of the ensemble other than ourselves. This focus-shift allows us to pick up on things that we may miss if we're focused on ourselves.
Just some basic things I think about, and some things we think about in Presidio to make the experience more enjoyable for the audience:
I conceal the emptying of my spit valve whenever possible. For me, that generally means rotating around and emptying the spit valve behind my leg. Audiences are weird about the condensation that comes from our instruments as they're not really aware that it's just water. Even our best attempts at concealment are sometimes met with an audience member after the show making a comment about gross it is
In Presidio, we make it a point to actually look at specific people in the audience and meet eyes if we are able. Additionally, we purposely shift our focus to various zones in the hall. Audiences LOVE to feel as though they personally connected with you, and it's pretty obvious to an audience member if you're looking AT them versus looking through them. If you're uncomfortable initially with eye contact, you can look at someones forehead,
There's so much to discuss! Always face the audience squarely. Trombonists have a tendency to want to play off to the right of a hall. This warps the sound for much of the audience, but also loses connection.
What to do when you're resting always comes up. In Presidio we analyze what each of us is doing when we may have a few measures rest. We usually find some way to stay engaged with what is happening on stage, even if that just means focusing on someone with a prominent line, smiling, nodding at them, etc.
Horn carriage at rest is big for the audience. What feels natural to us often looks unnatural on stage. Personally, I try to avoid holding the horn in front of me when resting. Having the instrument between your audience and your body can act as a barrier to connection. I try to hold my horn to the side.
As a general starting point, it's so valuable to video record yourself. One really powerful method is to record yourself and watch with the sound turned off. If you're visually engaging with no sound, you're on the right track.
Love this discussion! Audiences come to concerts to be entertained. How that happens can vary depending on the performance situation (academic recital, professional recital, chamber ensemble in academic vs. entertainment settings, etc)