At which rate does the leader pool rotate?

I noticed that the choices to pick from in the Stellaris leader pool seem to change from time to time.

What is the actual interval, when does it make sense to have a look at the possible "new recruits"?

Solution 1:

At the moment you hire a leader, a new one is added to the pool to replace the one you just hire.

The rate of rotation is quite unclear. According to this Steam thread and personal experience, the leaders from the pool change after a certain amount of time. Some people seems to think it might be when they died from old age. However, this hypothesis would mean rotation of leader with increased lifespan would be slowed, and immortal leader would not rotate at all. A more plausible hypothesis, based on the leader wiki page, would be that leaders are changed at 50 years old.

You can also manually change a candidate for the cost of 50 influence. You just have to hire and fire him instantly.