Engineer building tower, somewhat unfortunate if fell! (6)

I believe the answer is:

eiffel

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

'engineer building tower' is the definition.
'eiffel' can be an answer for 'engineer' (I've seen this before). I'm not sure about the 'building tower' bit.

'somewhat unfortunate if fell' is the wordplay.
'somewhat' says the answer is hidden in the clue.
'EIFFEL' is hidden in the letters of 'unfortunate if fell'.

Can you help me to learn more?

(Other definitions for eiffel that I've seen before include "French tower-designer" , "French structural engineer" , "& 21 Across Parisian landmark" , "French designer" , "Famous tourist tower in Paris" .)

I've seen this clue in The Times.

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