Well, if you can avoid it, I wouldn't recommend full-on unemployment unless the situation is really that bad. Work provides an intrinsic sense of daily purpose and routine that does help with psychological recovery, regardless of how one feels about it in the middle of burnout.

A part-time schedule could always be part of the burnout plan. Or a planned sabbatical. Like I said, do the creative thinking now so it's not when you're in the firefight.

You were working as an independent consultant.

I'm not even sure you need to pretend you were working. Especially mid-career, taking 6 to 12 months off to consider your options, do some learning, etc. isn't something I would think twice about as an employer.

"gaps in your resume" is actively used to cover over-40 hiring discrimination in tech jobs

Fair enough for some situations. I guess it helps that I've never had a job since school where I came in through HR as opposed to someone I knew.

I've done this a few times and never had a problem.

I put my time off front and centre. I learned Spanish, worked on side projects, taught myself self-reliance and the ability to overcome obstacles, etc. etc.