I’ve never died on camera, so I can’t answer for how it works in film or TV. I can tell you from onstage that there are a few tricky things about dying.
First off, holding your breath isn’t a good idea. You need to breathe slowly and calmly so that your rib cage doesn’t move, but if you try to hold your breath for more than about 2 minutes, you’re going to breathe whether you like it or not. Depending on what you were up to before you died, it can be really hard to find that calm breath - if it was a big fight scene, you may well be out of breath, which is fine if you get to die slowly, but if you have to die suddenly and be still after running up and down the barricade a la Les Mis, that’s hard! I think that’s why we were directed to go into slow motion at the end of the big barricade scene - to make it easier for everyone to slow down their breath. Enjolras got more time to calm his breath, but he also had to climb up and down the barricade about 6 times before he got shot. Fortunately, the focus was on Jean Valjean and Javert for much of it, but there was still a good 30 seconds of total silence and strong light where the least little twitch, swallow or fart would completely ruin the scene.
Try to die in a comfortable position - if you’re holding your body with tension, then that tension will eventually cause a twitch or a tremor.
This is a huge part of why Hamlet shirts (white so the fake blood can be boiled and bleached out, long sleeves and really baggy to help hide the movement of the chest.) are so popular onstage. It also helps that the focus will eventually shift to the people left alive onstage, and unless the lighting designer has been particularly cruel, usually the lights will go down on the dead guy to guide the story to those still telling it.
My (possibly wrong!) understanding is that in real life, the eyelids may need to be physically closed - onstage, this isn’t a good idea, as it’s a great way for someone to slip and put a finger in the eye of the dead actor, which usually gets a reaction.
There’s also a huge trust when you’re dead - actors like to arse around onstage, and the dead guy is a sitting target. Nothing like having someone yank out a nose hair or tickle you when you’re supposed to be past knowing… Yet another reason to always be good to your fellow performers - bad behaviour can come back to haunt you…