Show embarrassment about author being rather rude (6)
I believe the answer is:
bluish
'rude' is the definition.
Both the definition and answer are adjectives. Perhaps they are linked in a way I don't understand?
'show embarrassment about author being rather' is the wordplay.
'show embarrassment' becomes 'blush' (I've seen this before).
'about' indicates putting letters inside.
'author being rather' becomes 'i' (I can't justify this - if you can you should give a lot more credence to this answer).
'blush' enclosing 'i' is 'BLUISH'.
Can you help me to learn more?
(Other definitions for bluish that I've seen before include "colourful" , "shade" .)