OTOH globals tend to have a problem, if the line distance between creation and usage gets to big, or generally if scope and context are not easy to oversee.

I'd use a block scope to simulate an object², the "global" is used like a class-attribute.

{ 
  my $global="whatever";
  sub method1 { 
       ...;
       foo($global);
       ... 
     }
  sub method2 { 
       ...;
       bar($global);
       ... 
     }
  sub ...
}
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Closures are in most simple cases more elegant than objects, especially in perl¹!

(they just can't inherit, but that's not a "simple" case anymore).

UPDATES:

(¹) just compare to grandfathers lightweight object! No blessing, no $self ...

(²) "encapsulation" to be more precise