Not catching on

I’m doing a puzzle where you have to find the word linking three others, for example ‘house’, ‘sky’ and ‘weight’ are linked by ‘light’. Sometimes I can get a word linking two of the three, but I don’t know whether the remaining concatenation is nonsensical and I’m therefore wrong, or it’s just something I haven’t heard of. I started thinking about ‘on’, ‘tail’, and ‘wool’:

On, tail and wool…Ooh, cotton. Cotton wool, cotton tail! That must be it. On cotton? Why’s there always one I don’t understand? I wonder whether it’s just a badly made quiz. This seems to happen quite a lot. I…oh.

I suppose that’s a little irony, right there.