Bodega finally provided source for tequila (5)

I believe the answer is:

agave

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'source for tequila' is the definition.
I can't tell whether this definition defines the answer.

'bodega finally provided' is the wordplay.
'finally' indicates one should take the final letters.
'provided' becomes 'gave' (giving is a kind of providing).
The final letter of 'bodega' is 'a'.
'a'+'gave'='AGAVE'

Can you help me to learn more?

(Other definitions for agave that I've seen before include "Tropical plant" , "A cactus" , "Succulent; daughter of Cadmus" , "Spiky succulent" , "Succulent plant" .)

I've seen this clue in The Times.

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