$1 will not contain the word from the regex, because the special regex variables are automatically localized to the enclosing blocks. As perlre explains it:

       $<digits>
               Contains the subpattern from the corresponding set
               of parentheses in the last pattern matched, not
               counting patterns matched in nested blocks that
               have been exited already.  (Mnemonic: like
               \digits.)  These variables are all read-only.
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Since the while block has been exited, by the time you check $1 it contains the value it held before the while block was executed.

Try this instead:

my $value = 'not found';
while (<FILE>) {
    $value = $1, last if /TARGET\s?=\s?(\S*)\s/;
}
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