Well, you ARE outputting the "Hydrophobic stretch found" line each time there is a match:

while($seq =~ /([VILMFWCA]{8,})/g){ #search for desired sequence
    my $location = pos($seq); #find location
    my $length = length($1); #determine length

    print "Hydrophobic stretch found in: ", $header, "\n"; #printing o
+utputs for results
    print $1, "\n";
    print "The match was at position: ", $location - $length + 1, "\n\
+n";
}
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If you only want to print it once, the easiest way is to introduce a flag indicating whether it's already been output. Declare a new variable in front of your while loop there, and then check and set it inside the loop body:

my $header_printed = 0; # header for this thingamabob was not yet prin
+ted

while($seq =~ /([VILMFWCA]{8,})/g){ #search for desired sequence
    my $location = pos($seq); #find location
    my $length = length($1); #determine length

    unless($header_printed) {
        print "Hydrophobic stretch found in: ", $header, "\n"; #printi
+ng outputs for results
        $header_printed = 1;
    }

    print $1, "\n";
    print "The match was at position: ", $location - $length + 1, "\n\
+n";
}
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Obviously this could be written more concisely, but this way it's clear what's going on.

Does this help you?