Stimulate sensually, keeping it up well into the night (9)

I believe the answer is:

titillate

'stimulate sensually' is the definition.
(titillate can mean to arouse)

I don't understand the remainder of the clue.

(Other definitions for titillate that I've seen before include "provide excitement" , "create superficial interest" , "Excite or stimulate pleasantly" , "Excite pleasurably" , "arouse interest" .)

I've seen this clue in The Times.

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