Your code would be easier to read if you used consistent indentation - honest! It will also help you if you always use strict; and use warnings;
The use of quotes is part of your problem. The \ is an operator, and \ has no effect inside double quotes. Update: that's rubbish, of course it has an effect, what was I thinking?

Here is my version, with some variables added to make it work:

use strict;
use warnings;

sub GetDecUser {

    my $LFILE;
    my $LOGFILE12 = $0;
    my @arr12 = ('The','quick','brown','declared users');
    my @arr10 = qw(The quick brown fox);
    
    if (-e $LOGFILE12) {                     
        $LFILE = \@arr12; # if the 12 log exists, use it         
    } 
    else {
        $LFILE = \@arr10;                 
    }
    
    print "$LFILE\n";    

    for my $dec (@$LFILE)    
    {
        if ($dec =~ /declared users/)          # match this
        {
            print "TESTING we found it: $dec\n";    
        }
    }
}

GetDecUser();
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