Changing one's mind about narrow ruler (10)

'changing one's mind' is the definition.
('rethink' can be a synonym of 'change one's mind')

'about narrow ruler' is the wordplay.
I cannot really see how this works, but
'about' could be 're' ('re' means regarding or about) and 're' is located in the answer.
'narrow' could be 'thin' (associated in meaning) and 'thin' is found within the answer.
'ruler' could be 'king' (king is a kind of ruler) and 'king' is found in the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?