This topic seems to arise frequently enough to warrant a somewhat "all encompassing" set of solutions. There are three fundamental ways to hide a shape: 1.) toggle its visibility, 2.) assign it to a specified layer and toggle the layer visibility, and 3.) shrink it to zero size. The 3rd method works well for "images" that are imported. The attached file covers methods (2) and (3).
The file was updated today to allow toggling the visibility of a layer on a different page, in this case, the background page. There are two approaches provided, the first is uses actions response for when right clicking anywhere in the page, and the 2nd uses a dedicated shape. Either way, a list of layers could be incorporated.
Check out the shapesheets for specific syntax.
HTH
Wapperdude
nice