I have lights at the top and bottom of the stairs.
They both come on at once via switches top and bottom in the usual 'common'
arrangement'. This is how it's meant to be.
The bulb at the top on the landing appeared to have failed. I changed it,
still no joy.
With the landing bulb in place, but not working, I found that the lower bulb
would not go off, using either switch.
Also the bathroom bulb fitting seems to have failed.