Yes, I should have given the Win32::GUI context ... eyes glazed over from lengthy fruitless search before finally posting this question resulted in tunnel vision.
v1.06 of Win32::GUI is in use here as well, not the older version packaged with LOFT. I've used the ploy of creating an invisible dummyButton which gets clicked or pushed under program control at the end of the Click handler for the button I want to pop, but neither of those events do it; control transfers to dummyButton's handlers without any change in the visual appearance of either Button. And that makes sense to me (though I'd hoped for some luck) because the calls to dummyButton occur in the context of the handler of the Button I want to release.
As for the code I'm not showing; that's exactly the problem. Suppose I take control of any event of any button; what code will then trigger redrawing of a button pushed? Short of looking into Win32 itself, I can't find anything in the Perl environment.
I hope I'm getting this across more successfully now.