Waterclocks either with a set amount of water if all dogs are being given the same time to try to beat (as in agility), or to empty in some sort of calibrated way to work as medieval stopwatch (for coursing/tracking trials).
In medieval cookbooks, one sees instructions such as "stir it for as long as it takes to say 3 Our Fathers", i.e. to recite the Lords Prayer three times. So for relatively short intervals, such as agility courses that run in only about a minute, having the crowd recite (or sing?) something to time the event could be fun - like a period equivalent of the Jeopardy theme song. (something like Sumer is icumen in - [])