Is there a method to have Tk::Optionmenu start displaying the option list without having the user first click the button?

Yes, generate a tk event, or call the appropriate Tk::Optionmenu method directly, Tk::WidgetDump might help you figure stuff out

or, use a widget other than Tk::Optionmenu, maybe a Tk::Listbox or something else, like a frame or panel of buttons that you create

Question 2: Why does the Optionmenu callback function (localCall below) get called before the user click of Optionmenu button?

What does the documentation say about it? https://metacpan.org/pod/Tk::Optionmenu#command

I would assume because the Tk::Optionmenu calls it, because its written that way :) ... and this is probably a bug but it might be a feature; -options is loaded and a default option is selected after the -command is bound ... so the -command callback gets invoked

Please look at my workaround.

Yup, akward :) I don't recognize any part of the program as a workaround

In each callback you can use $Tk::event and $Tk::widget ... combine with ->parent, and no need for some of those closures