How did the phrase “if you’re a priest, with the line you’ll go!”

The popular proverbial expression “if you’re a priest, with the line, you’ll go”, is said to show that someone should be waiting for him…
suitable time, in order to do something, without any exception.
The phrase we most well-known Theodoros Kolokotronis, and from then on it stayed.
It was called, in the old times, mainly in mills and taps, waiting to turn people to grind or get a crock of water.
So, when they saw a priest doesn’t want to comply with the order, the name of the phrase.