Crossword Genius

Twelfth Night fool shows fever plus backchat (9)

Ross

I believe the answer is:

aguecheek

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'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".)

I've seen this clue in the Sydney Morning Herald.
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