Thank you Monks, for all your great suggestions to my recent question. The approach I took was to move the MainFunction block below the definition of the package ScopeTest. This solved the problem nicely. I've added the final code to the bottom of this post.

tobyink clarified the difference between lexical variables and package variables, which I think I now understand. In the code below, I added a second print statement in MainFunction{}.

print("DumpValue: sv_a ... $ScopeTest::sv_a\n");

Now, if the variable $sv_a is declared as my $sv_a = ..., then the message "Use of uninitialized value $ScopeTest::sv_a ..." is displayed and the program fails. But, if the variable $sv_a is declared as our $sv_a = ..., then the program runs just fine without any errors.

The final working code with $sv_a declared as a package variable is now:

#!/usr/local/bin/perl
use 5.010;
use strict;
use warnings;

package ScopeTest;
 our $sv_a = "scalar variable A";

 sub dump_sv {
   print("DumpValue: sv_a ... $sv_a\n");
 }

 sub new {
   my $obj_hv = {};
   bless($obj_hv, $_[0]);
 }

package main;

MainFunction: {
   my $t_obj = ScopeTest->new();
   $t_obj->dump_sv();

   print("DumpValue: sv_a ... $ScopeTest::sv_a\n");
}
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