I have taken the back panel off and there aren't any signs of dirt/corrosion on the circuit board. There are a few keys which do this and on each of them they trigger a total of 8 notes. The resistors on the circuit board are also grouped in 8 so I don't know if there's some kind of shorting happening (I'm not particularly technical)
I also noticed that on the pads which detect the key press (two per key), I can lay a finger across a pair and trigger a note, but with the failing ones instead of playing a group of 8 there is no sound at all when I try the finger technique on them. However, doing the same with the rubber pads which sit between the circuit board and the keys, I get the 8-note cocophany.
The keyboard is already 25 years old so I don't have high hopes for it, but if it's a relatively easy fix I'd like to rescue it!