Ok, got it done. Not housing, not brushes, not bearings. Upper clamp screw of the coupling was rubbing against the coupling cover.
It is quite funny: when I put my ear against the hub, I heard squeaking in the hub. When I leaned over the steering box in the engine bay - I heard it in the steering box. This steering spindle jacket works as resonator tube...
So layer after layer - removed the steering wheel and brushes - squeaks. Removed the bearing holder with both bearings - squeaks. Unscrewed and slid up the coupling cover - no squeak.
I removed the screw. I do not think I have a standard one - allen head screw appeared to be too high, so I took some of it on the grinder. Being there, I removed the spindle and properly lubricated the plastic sleeve as BBB says, because, honestly, I forgot to do it when I fitted it before.
Perhaps I should have inserted a shim between steering box and frame? Or maybe I just have a wrong screw there...