Funny old cure for water on the brain (3)

I believe the answer is:
tap
This might be a double definition.
'funny old cure' is the first definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Maybe they are linked in a way I don't understand?
'water on the brain' is the second definition.
'tap' can be an answer for 'water' (tap water is a kind of water). I'm unsure of the 'on the brain' bit.
'for' is the link.
Can you help me to learn more?
(Other definitions for tap that I've seen before include "Flow controller; knock" , "Water controller" , "Obtain money from" , "water supply" , "Secret (phone) intercept" .)
