Yes, of course. And yet, having a gap on a resume is also something people make judgments about.

Yes, and given that being without employment (really, without income, but those are equivalent for most people) for long enough is literally a life or death situation, you're fully justified in that by lying about it in self defense. If you're privileged enough that not having any income for an extended period isn't a big deal, then, so what? But, if you aren't, lie.

So don't leave a gap. Do I have to write the .tex for you myself?

Apparently. I generally don't include lying in my toolbox.

You don't need to lie, but you also don't need to disclose every single thing to your new employer. If you had a short stint at a company, just leave it off. If they ask, just say you took some personal time to figure out what you wanted to do next. I think that's a totally valid description of trying a new job that didn't work out. I know a lot of people who have taken years off for fun. No one questioned it.

You should. You're at a disadvantage if you don't, because everybody else sure does.

"Fire fast" can mean you get canned after a 6 month probation period (I know I was at one place). Explaining a 6 month gap is just barely possible if you leave it off, two of those in a row and it's a substantial chunk of anyone's career.