Desperately looking for processed cheese in search engine (10)

I believe the answer is:

beseeching

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'desperately looking' is the definition.
The answer and definition can be both to do with communicating as well as being present participle verbs.
Perhaps they are linked in a way I don't understand?

'processed cheese in search engine' is the wordplay.
'processed' indicates anagramming the letters.
'in' indicates putting letters inside.
'search engine' becomes 'Bing' (Bing is a search engine).
'cheese' is an anagram of 'eseech'.
'eseech' going into 'bing' is 'BESEECHING'.

'for' is the link.

Can you help me to learn more?

(Other definitions for beseeching that I've seen before include "Pleading" , "Begging" .)

I've seen this clue in The Irish Times.

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