Going on and on about the mad sister being shut up (10)

I believe the answer is:
persistent
'going on and' is the definition.
I can't judge whether this defines the answer.
'about the mad sister being shut up' is the wordplay.
'about' indicates putting letters inside.
'the mad' indicates anagramming the letters.
'being shut up' becomes 'pent' ('pent' can be a synonym of 'shut up'**).
'sister' anagrammed gives 'ersist'.
'ersist' placed within 'pent' is 'PERSISTENT'.
'on' is the link.
Can you help me to learn more?
(Other definitions for persistent that I've seen before include "Resolute - interminable" , "Determined" , "hanging on" , "Lasting, prolonged" , "not giving up" .)
