In New Zealand most of the pedestrian crossings don't show any lights until someone pushes the button. Occasionally someone will stand at the lights staring at a completely unilluminated crossing light until someone else pushes the button.
Handily it means if the light is on it will change.
Yeah, the 'don't walk' light doesn't illuminate until you press the button, there are even some pedestrian only lights where you must both press the button and stay standing on a mat, otherwise the light will not change.
I've never seen a traffic light in New Zealand that won't change it cycle in some way during at least some part of the day when that button is pressed. During peak hours there are many traffic lights where the cycle doesn't change at all when you press the button, other than show the walk.
Most other traffic lights modify their cycle slightly, with red turning lights to prevent drivers from turning across the crossing pedestrians.
The button is only truly important outside of peak hours, when the traffic lights operate on sensors. And the cycles for cars are often so short that a pedestrians can't actually cross the road in time. So pressing the button not long makes the cycle change, but lengthens the cycle.
Handily it means if the light is on it will change.