I think I once read an interesting term for "rule through courts" in reference to Islamic/sharia courts (which also had some tribal significance iirc) in Somalia who acted as the de facto after the central govt collapsed. I can't find it again.
Kritarchy. Both the phenomenon and the word are pretty rare.
> judiciary monarchy of sorts
Do they have mandates for life?
Yes. Supreme court judge mandates are essentially lifetime. There's no fixed term, only way they leave is when they're forced to retire at 75 years old. They're just now trying to limit it to 8 years.