Depends on what features they have and how they are set up.

Where I live there are a few very different setups.

Some crosswalks have no buttons and automatically activate each times the lights cycle on a set pattern.

Some have a button and if you press it the cross traffic light will most likely change on avout 30 seconds and you will be able to cross. If you press it immediately after it chsnges back you have to wait a couple minutes, but not a long time.

One that I use doesn't change the stoplight rotation but pressing the button is necessary for the crosswalk light to come on and it keeps cross traffic from getting a green light as fast as when the crosswalk isn't used. The intersection used to stop cross traffic when you pushed the button and I have no idea why they changed it.