I think this situation is a good candidate for using exported symbols. Have package moduleA export $readMode, etc. which other modules can import. The implementation would go something like:

package moduleA;

@ISA = qw(Exporter);
@EXPORT_OK = qw($readMode $writeMode $appendMode openFile);
$readMode = '';
$writeMode = '>';
...
1;
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use moduleA qw($appendMode openFile);
...
# calls moduleA::openFile() with parameter $moduleA::appendMode:
openFile(..., $appendMode); # note: no namespace qualifier needed
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