Hello. This will be a rather short response: Mr Socrates in Bill and Ted spoke anachronistically- the earliest evidence of the hourglass in the form that we understand do not emerge until the early medieval period. The Greeks instead used something called a Water Clock or Clepsydra. They were a more rudimentary version, a picture of an existing one in the Athens Archaeological Museum which can be found here: https://en.m.wikipedia.org/wiki/Water_clock#/media/File%3AAGMA_Clepsydre.jpg

The design is rather simple yet effective, one pot is placed above another, the pot above has a small hole punctured in at the bottom. Water is poured into the top one and, like a sieve, water slowly trickles into the pot below. This gave them a consistent and reliable way of measuring an allotted amount of time. As you can imagine these were used for a variety of domestic and commercial reasons much the same as a traditional hourglass.

As an interesting anecdote: in Athenian legal cases it was important for both the defendant and accuser, as well as any witnesses, to be given an equal amount of time to speak as they believed this would ensure a fair process. And so they used one of these water clocks to time each speaker, once the water had drained your time was up. A parody of a court case can be seen in Aristophanes’ play the Wasps where he mocks a real trial between the demagogue Cleon and another Athenian general called Laches for supposed malfeasance during a campaign to Sicily around 425 BC during the Peloponnesian War.

Another far more interesting and relevant anecdote for Socrates in particular that slipped my mind until I hit send: Plato was said to have invented an early version of an alarm clock by modifying the water clock with some sort of device that produced a sound similar to a water organ. He used it to signal when his lectures were starting in the morning and evening.

Athenaeus mentions (Philosophers at Dinner, 4.174c) that:

“It is said that Plato provided a small notion of its construction by having a clock for use at night that was similar to a water organ, although it was a very large water clock.”

Considering Plato is Socrates’ student perhaps he would have made one as a gift to his beloved teacher? One can only assume!

Hope this helps!

Edit: added the info about Plato’s alarm clock.