both the vert and horz lock are weak then its prob a defect sync separater.
If it syncs better with a weak signal, then it could be a problem with the AGC setting.
My guess is the sync separater OR the noise inverter Or the sync output.
the reason being its effecting both vert and horz.
I am assuming you have not messed with the AGC or noise inverter settings. Best not to do that unless you know what you are doing.
The best way to determine the problem is the use of a scope, checking the output from the sync separater. Otherwise its pretty much just blind checking.
as a minimum you could try a new a new noise inverter tube/sync sep tube/sync output tube to see if that helps.
the sync lock on this sets should not be the slightest bit critical.
the fine tuning will have a lot to do with it as well. I presume you have tried that to see if it helps. this generally shows up as a dark pic that loses sync
https://www.youtube.com/watch?v=RAk9lKv03zA