Dropping off, like some acquaintances? (7)

I believe the answer is:

nodding

I believe this is a double definition.

'dropping off' is the first definition.
(both can mean falling asleep)

'like some acquaintances?' is the second definition.
(as in a nodding acquaintance)

(Other definitions for nodding that I've seen before include "making careless mistakes" , "Signing agreement" , "Letting one's head drop" , "being agreeable?" , "Signalling assent" .)

I've seen this clue in The Times.

Want a hint initially instead of a full solution? Install my app