You don't wait for a star to undergo its maximum parallax displacement. Parallax is measured by observing a star's position at two different points in Earth's orbit around the Sun, typically six months apart.

Here's why:

* Parallax is a measure of apparent change in position: Parallax is the apparent shift in the position of a star due to the Earth's movement around the Sun.

* Maximum displacement occurs at opposite ends of Earth's orbit: The largest apparent shift (maximum parallax) happens when the Earth is at opposite points in its orbit around the Sun. This is why observations are made six months apart – to capture the greatest possible difference in perspective.

* It's not a continuous process: The star itself isn't moving to a different location. The apparent shift is an illusion caused by our changing viewpoint.

In summary, you don't "wait" for a star to undergo maximum parallax displacement. You observe it at specific points in Earth's orbit to measure the maximum displacement.