Engineer cried about every single phone feature (6,2)

I believe the answer is:

caller id

I'm a little stuck... Click here to teach me more about this clue!

'phone feature' is the definition.
(I've seen this in another clue)

'engineer cried about every' is the wordplay.
'engineer' is an anagram indicator.
'about' is an insertion indicator.
'every' becomes 'all' (similar in meaning).
'cried' with letters rearranged gives 'cerid'.
'cerid' enclosing 'all' is 'CALLER ID'.

'single' is the link.
I am not very happy about this link. It may be part of another bit of the clue.

Can you help me to learn more?

I've seen this clue in The Times.

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