Damp patch on stairs wall

Interesting problem on the stairs wall about 3 feet up from the floor, a damp patch that never dries, I've had to pull off the wall paper in that section.
its a terraced house old about 1800, old sandstone walls its 2nd to the last in the row.
i'm guessing the last houses chimney is leaking as his chimney breast would be in the same position as mine and the other side of it, its roughly where the damp patch is, I've talked to my neighbour but the guy doesn't want to know as hes just moved in.
Ill have to take the plaster off to investigate the wall itself and hopefully find where the moister is coming from.
What will be my options ? paint on some sort of water barrier solution and re plaster ?

If it’s the chimney then only fixing that will rectify the problem.

I've offered to pay but hes not interested as its his chimney. Its only damp in one section about 1 foot in diameter about 2 foot off the 3rd step on my side. There is no damp either side or above it, i've taken off all the plaster above and below that section, im waiting to see if it dries out, my neighbour must have found damp as hes painted damp sealer on his side as ive smelt it for 2 days. I guess my only option is to do the same.