The button counter? (10)
I believe the answer is:
calculator
This clue could be a double definition.
'the button' is the first definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Maybe they are linked in a way I don't understand?
'counter?' is the second definition.
(counter is a kind of calculator)
Can you help me to learn more?
(Other definitions for calculator that I've seen before include "Adding machine" , "Sum-doer's aid" , "Ready reckoner" , "See 12" , "this should provide some answers" .)