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Makes mistake, suggesting they should eat while covering mouth? (5,2)

Ross

I believe the answer is:

slips up

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'makes' is the definition.
The definition and answer can be both related to thinking as well as being verbs in their -s form.
Maybe they are linked in a way I don't understand?

'mistake suggesting they should eat while covering mouth?' is the wordplay.
I cannot quite see how this works, but
'mistake' could be 'slip' (a slip is a blunder or mistake) and 'slip' is present in the answer.
'eat' could be 'sup' (supping is a kind of eating) and 'sup' is found in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for slips up that I've seen before include "falls over" , "Makes a mistake" .)

I've seen this clue in The Irish Times.
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