The phrase ‘an incense stick of time’ grew to popularity due to it’s popular use in a genre of Chinese fantasy novels known as Xianxi.
In these books, the phrase is used to describe a brief passing of time, which can be anywhere from 5 minutes to an hour.
The origin of this phrase is likely rooted in ancient Chinese history. In some regions, incense was crafted to strict formulations in order to ensure that the incense burns for a specific amount of time. This allowed them to know roughly how much time had passed, and served the same purpose as modern timepieces.
It’s worth mentioning that most modern incense sticks will typically burn for 20 to 60 minutes, depending on what type of incense it is.