You can actually encode your rules into a regex, which will show all possible interpretations.

(The trick is to force backtracking with a (*FAIL) )

And it highlights what hippo already told you: you get two possible results for the case of 13 digits!

IOW you need more filter rules, like ...

• a valid check digit
• impossible serial numbers
• chronological entries
• consistent format per file
• whatever other heuristic ...

And then you must hope there are no more ambiguities left ...

But I think this is a good start.

use v5.12;
use warnings;
use Data::Dump qw/pp dd/;


while (my $l = <DATA>) {
    chomp $l;
    my ($n,$desc) = split /\s*=\s*/,$l;
    say "--- $n";
    say "    $desc";
    my $year  = join "|", 18..22;
    my $month = join "|", 1..9, "01".."12";
    my @res;
    $n =~ /^
           (?:
               (?<year>$year)
           |
               (?<month>$month)         # no month without year
               (?<year>$year)
           )?                           # date is optional
           (?<serial>\d{10})
           (?<check>\d)?                # check is optional 
           $
           (?{ push @res, { %+ } }) 
           (*FAIL)
          /x;
    say pp \@res;
    warn "*** TOO MANY MATCHES $n***\n",pp(\@res),"\n\n" if @res > 1;
    warn "*** NO MATCH $n ***"     if @res < 1
}

__DATA__
1231600014       = 10 digit version (just the core serial)
221231600014     = 12 digit version (minus both leading month and last
+ check digit)
1221231600014    = 13 digit version 2 (minus the leading zero for the 
+month and minus the check digit). These entries would need to be corr
+ected to add the leading zero and therefore become the 14 digit versi
+on
2212316000140    = 13 digit version 1 (minus the leading 2 month digit
+s but including the last check digit)  
01221231600014   = 14 digit version (minus the last check digit)
012212316000140  = Full 15 digit serial. This comprises of month and y
+ear (0122), core serial (1231600014), check digit (0)
[download]

*** TOO MANY MATCHES 2212316000140***
[
  { check => 0, serial => 1231600014, year => 22 },
  { month => 2, serial => 2316000140, year => 21 },
]

--- 1231600014
    10 digit version (just the core serial)
[{ serial => 1231600014 }]
--- 221231600014
    12 digit version (minus both leading month and last check digit)
[{ serial => 1231600014, year => 22 }]
--- 1221231600014
    13 digit version 2 (minus the leading zero for the month and minus
+ the check digit). These entries would need to be corrected to add th
+e leading zero and therefore become the 14 digit version
[{ month => 1, serial => 1231600014, year => 22 }]
--- 2212316000140
    13 digit version 1 (minus the leading 2 month digits but including
+ the last check digit)  
[
  { check => 0, serial => 1231600014, year => 22 },
  { month => 2, serial => 2316000140, year => 21 },
]
--- 01221231600014
    14 digit version (minus the last check digit)
[{ month => "01", serial => 1231600014, year => 22 }]
--- 012212316000140
    Full 15 digit serial. This comprises of month and year (0122), cor
+e serial (1231600014), check digit (0)
[
  { check => 0, month => "01", serial => 1231600014, year => 22 },
]
[download]

update

refined the month rules by substituting \d|\d\d with $month = join "|", 1..9, "01".."12";