Thanks, that did the trick. After a reboot the 2nd DNS server was added to /etc/resolv.conf.
Can not recommend this method though, because after rebooting my Toon I was seeing packet loss / timeouts and high ping times (> 4000ms) to my Toon. Altough troublesome, I succeeded in SSHing to my Toon, move the script out of the /etc/rc5.d folder and rebooted my Toon. After rebooting my Toon was functioning normally again. To make sure it was caused by the script I repeated the process and concluded that the issue was indeed caused by the script (was seeing high ping times and dropouts again).
I won't be adding that 2nd nameserver anymore, it's not worth the trouble...
Thanks anyway TheHogNL!