I tell the TSA agent who runs the porn machine that I want to opt out. Sometimes there's a TSA agent directing traffic before that, so I'll tell them instead.
They usually make sure that they know which of my shoes and carry-ons is going through that separate scanner so I can pick it up after. I end up waiting at most a minute for a male (because I am male) TSA agent to come over and do the pat down. Before they do the patdown, they explain what they're going to do; I believe this explanation is standardized and memorized, though I haven't gone through word for word and checked that. Afterward they'll either swab my some area of my clothes, or (more often) swab the nitrile gloves they patted me down with, and put it in what I assume is a spectrometer to check for chemicals. Twice, the person doing the pat down was a trainee, so the pat down was observed by a trainer and the trainer asked me a few questions, like if I felt the trainee had used too much pressure during the patdown. At that point I'm free to pick up my bins of shoes and other carry-ons, and I'm free to go. Entire process takes 2-5 minutes, most often in the lower end of that range.
During the patdown, some agents will ask questions like where I'm flying to and why. This is pretty hit or miss and I don't get the impression that they're part of the security (though it could be). The impression I get is that it's just making small talk on the most obvious available topic.
You just tell the TSA agent that you want to opt out of the body scanner. They then find an agent of your gender to do a pat-down screening and a swab to test for trace chemicals. It takes about 3 minutes assuming they have an agent available.
I used to opt out (before I got TSA pre). When you're standing at the rapey scan and they tell you to go through, just say "opt out". Then they'll exhale loudly, roll their eyes, and yell "opt out". Then you stand around for a couple minutes while they find somebody to give you an old handy. They'll read you their spiel and ask if you want a private room (I assume that involves a happy ending). Then they ask if you have any sensitive areas, do a half-assed job of patting down your upper body, run their hands up and down your legs, and wipe their gloves to test for bombs or farts or whatever.
I vaguely remember the yelling "opt out" in the early days of the porn scanners, but I don't think they do this at most airports any more.
I think you might be taking the agents' reactions more personally than they are intended: I'm sure that the TSA agents aren't necessarily happy because you're adding a task to their plate, and in busy airports they already have a lot going on, so it's understandably visible that they're stressed. But every one I've interacted with has kept it more professional than an eye roll.
Remember, the agents themselves are just not-all-that-well-paid workers. They aren't the cause of the problem.
They usually make sure that they know which of my shoes and carry-ons is going through that separate scanner so I can pick it up after. I end up waiting at most a minute for a male (because I am male) TSA agent to come over and do the pat down. Before they do the patdown, they explain what they're going to do; I believe this explanation is standardized and memorized, though I haven't gone through word for word and checked that. Afterward they'll either swab my some area of my clothes, or (more often) swab the nitrile gloves they patted me down with, and put it in what I assume is a spectrometer to check for chemicals. Twice, the person doing the pat down was a trainee, so the pat down was observed by a trainer and the trainer asked me a few questions, like if I felt the trainee had used too much pressure during the patdown. At that point I'm free to pick up my bins of shoes and other carry-ons, and I'm free to go. Entire process takes 2-5 minutes, most often in the lower end of that range.
During the patdown, some agents will ask questions like where I'm flying to and why. This is pretty hit or miss and I don't get the impression that they're part of the security (though it could be). The impression I get is that it's just making small talk on the most obvious available topic.