One way to do it is to change what constitutes a "line end". In this case ! looks like a good character to choose as a line end character. Consider:

use warnings;
use strict;

$/ = '!';

while (<DATA>) {
    next unless /ip address (?:\d+\.){3}\d+/;
    
    next unless /interface (\w+(\d+))/;
    
    print "$1 -> $2\n";
}


__DATA__
interface Vlan1
 no ip address
 no ip route-cache
 shutdown
!
interface Vlan12
 ip address 68.142.192.79 255.255.255.0
 no ip route-cache
 shutdown
!
interface Vlan8
 ip address 68.142.192.79 255.255.255.0
 no ip route-cache
!
[download]

Prints:

Vlan12 -> 2
Vlan8 -> 8
[download]