Intimate with Theodore, keeping sexuality secret (8)

I believe the answer is:

closeted

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'sexuality secret' is the definition.
'closeted' can be an answer for 'secret' (I've seen this before). I am not certain of the 'sexuality' bit.

'intimate with theodore' is the wordplay.
'intimate' becomes 'close' (similar in meaning).
'with' is a charade indicator (letters next to each other).
'theodore' becomes 'ted' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'close'+'ted'='CLOSETED'

'keeping' acts as a link.

Can you help me to learn more?

(Other definitions for closeted that I've seen before include "Shut away for private talk" , "Concealed" , "Shut in small room" , "Cedes lot, being shut away" , "Confined to a small space, as for intensive work" .)

I've seen this clue in the Sydney Morning Herald.

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