Thanks both.
Vamitul -- Well, yes. I now have separate PNGs that need to be in the script's folder. But I'd rather have everything in the script file. Besides, If I can't get something to work I want to know if it's really not possible 
Marc -- That example where a graphic is replaced immediately was just to show the problem. What I'm after is a checkbox such as some of InDesign's checkboxes, which can show either of three states: on, off, or mixed.
var icon_on = File ('. . ./checkbox_on.png');
var icon_off = File ('. . ./checkbox_off.png');
var icon_mixed = File ('. . ./checkbox_mixed.png');
var w = new Window ('dialog'); var icon = w.add ('image', undefined, icon_on); icon.id = 'on'; icon.addEventListener ('click', function () { switch (this.id){ case'on' : {this.id = 'off'; icon.image = icon_off; break} case'off' : {this.id = 'mixed'; icon.image = icon_mixed; break} case'mixed' : {this.id = 'on'; icon.image = icon_on} } });
w.show();
This script works fine. But I can't get it to work with string variables for the icons. I rummaged around with various variants of your solution, but I guess I'm missing something because I can't get it to work.
Thanks,
Peter