It seems Google Remote Desktop, a Chrome extension, does not work properly with Buster + Mate. I haven't tried with Bullseye, which is not an option in the environment concerned due to CUPS bugs, but in Buster there is about 5 seconds of remote-mouse-movement then no more.
Does anyone know of a way to fix this, or any other approach that might work through a mobile broadband router (at the 'controlled' end) where there is no option to fwd ports? Thanks, Gareth