Peduncle, pedicle, pedicule, pedicel - a range of post-classical latin formations all of which might be used to refer to the narrow part of structure consisting of two larger elements joined together.
None of the references I checked mentioned hour-glasses, so I trotted off to have a look at the definition of hour-glass just in case. Well, well, there it is, the OED definition of hour-glass includes the word used for that narrow part:
A contrivance for measuring time, consisting of a glass vessel with obconical ends connected by a constricted neck [...]