How to request a vacation hold on my AT&T phone plan?

There is no option not to be charged at all.  AT&T has never had that option.  The only way to avoid being charged that all would be to cancel your service.

AT&T stopped doing reduced rate vacation holds a couple years ago. At&t used to reduce the line charge to $10 for up to 6 months. However you still had to pay installments. And if you had installments with bill credits the bill credits were voided.

So if you contact AT&T to suspend your service you will have no service but will still have to pay the same amount you usually do. If you don't have any installments, you can always terminate your service. If you want to keep your phone number port it to Google voice.  .

I see posts from people all the time who suspend their service while they're outside the USA and then discover they need access to their phone number. There's a lot of two factor authentication that's tied to our numbers as well as other services like iMessage.  

If you don't want to pay for international day pass, or get charged pay-per-use charges, turn your AT&T SIM off.