You don't have to call support.
Just go to your profile settings and set your Gamertag to "Silver".
The currently paid subscription will still need to run out (so you will still waste the Gold status for the rest of the month you already paid), but after that you won't get billed for another month.
After you return, you can then turn your Gamertag status to Gold again, and Microsoft will then start to bill your Credit Card again, until you choose to go Silver again.
No need to call Customer Support or anything like that.