I assume that the main timeline of the scene is triggering the changes, and not the persistent symbol itself. (You may have the best results driving it all from the persistent symbol!). But given that....
Symbols can't directly stop timelines, because they don't have specific knowledge about how or where they are placed until they are running. However they can do this in an indirect manner, using Custom Behaviors. Here's the basic setup:
- For each scene, add a custom behavior that has the same name. This should have an action that will pause the timeline that is controlling the automatic advance
- In the persistent symbol, have the button use an on mouse click action to trigger custom behavior, and use the name of the custom behavior that you used in each scene in step #1
Now the persistent symbol will trigger the custom behavior, and whichever scene you are on will respond and run the action to pause.