The phrase “olive juice” is a misnomer.
Occasionally you will see it used to refer to the brine of preserved olives, when called for in a mixed cocktail such as a dirty martini.
You can actually buy it now in jars for bar use. It comes without the actual olives in it.
Elsewhere, the phrase “olive juice” is a mistranslation.
You will often see it where a piece was first written in Italian or Spanish, and then translated into English.
What is meant is olive oil. Olives do not contain enough water to give off anything that an English speaker would call actual juice from the fruit.