When code doesn't do what you expect it to do,

• Make sure the path of execution taken is the path of execution you expect the code to take. Investigate discrepancies.
• Make sure variables hold the value you expect them to hold. Investigate discrepancies.

There are two more errors in your code:

• /[A-Za-z]*/ successfully matches the first 0 characters of $fullString, not what you want it to match.
• Since there are no captures in /[A-Za-z]*/, it returns 1 on success even in list context.

$string contains "1", and thus $TAGS{$string} is undef. Fix:

    my ($string) = $fullString =~ /([A-Za-z]+)/;
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(I moved the my. There's no reason for it to be on a separate line.)