I am searching for manager jobs (software engineering management). Is there any advice for how to find a job that says it practices manager-tools approach for management? I am guessing that will more likely be a place that shares similar values. I don't think manager-tools.com has some "job postings" section (I wouldn't expect that), so it leaves me guessing if there is such a company that wholesale tries to follow this model.

Several ideas
1/ Post here, asking for leads to firms in whatever locations you find interesting.
2/ Check show-notes and podcasts for mentions of companies trained. (eg SpaceX)
3/ Check "Things I Think I Think" and its successor "Things We Think We Think" for mentions as well.
4/ Attend a nearby "Effective Manager Conference" training and network there.
5/ If there's a local Manager Tools meet-up, or you can start one, try that too.
6/ Name-drop Mark Horstman and Mike Auzanne in your interviews. If the interviewer perks up, that's a great sign. ;-D
In reply to Several ideas by Joseph Beckenbach
I like those ideas. Well
I like those ideas. Well done.