One problem with doing the disable alone is that it does not completely prevent multiple click events from occurring. If the app is busy, a second click could be done before the first click is handled and the button is disabled. Scripts such as Autohotkey for windows can also send the events despite the disabled-ness of the button.

The better way to go about this, is to check whether there is already a listBrowse widget in existence. If one already exists, you can destroy the old one and replace it, or skip the creation of a new one, whichever makes the most sense.

As for storing the flag as in the OP's original plan, all you should need is a variable that is scoped to cover the right region:

...
{ # Extra scope to keep $menuPopped contained to just this region.
  my $menuPopped = 0;
  sub thatReadsFlag
  {
    ...
    if ($menuPopped) {}
    ...
  }
  sub thatWritesFlag
  {
    ...
    $menuPopped = shift;
    ...
  }
}
...
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