NOTE: While it doesnt show here there is a character between the two quotes in my $a='';

use strict; use warnings; 
my $a=''; # entered by holding down cntrl pressing _ (shift+-) 
print "ord:".ord($a)."\n";
print 'hex:'.unpack("H*", $a)."\n";
my $b="\x1f"; 
if ($a eq $b) {print '$a eq $b'."\n";} 
exit;
[download]

result

ord:31
hex:1f
$a eq $b
[download]

but!!

#use strict; use warnings; 
my $a=''; # entered by holding down cntrl pressing _ (shift+-) 
print "ord:".ord($a)."\n";
print 'hex:'.unpack("H*", $a)."\n";
my $b="\x1f"; 
if ($a eq $b) {print '$a eq $b'."\n";} 
my $bb=\x1f; 
print $bb."\n";
[download]

Result

ord:31
hex:1f
$a eq $b
SCALAR(0xa3e67c)
[download]

so did you try printing \x1f or "\x1f" ?