Twelfth Night fool shows fever plus backchat (9)
I believe the answer is:
aguecheek
'twelfth night fool' is the definition.
I don't know anything about this answer so I cannot tell whether this works.
'fever plus backchat' is the wordplay.
'fever' becomes 'ague' (illness causing fever).
'plus backchat' becomes 'cheek' (I can't justify this - if you can you should give a lot more credence to this answer).
'ague'+'cheek'='AGUECHEEK'
'shows' acts as a link.
Can you help me to learn more?
(Another definition for aguecheek that I've seen is " Shakespearean role".)