Other answers have clearly pointed that the key is this case is negotiation. It is up to you, with the help of the others' considerations, to decide whether to be available or not. Also consider what your law says. You may like to add a tag that indicates the jurisdiction you are working in (e.g. united-states).
In my answer I would like to propose a different aspect of negotiation. Since question explicitly cites that having access to media resources costs money, tools could be another argument.
As soon as you decide to be available, immediately agree with your boss to provide you with a company phone with a SIM card enabled to roaming. This simplifies things a lot, particularly when you agree that you will turn off the phone at night or non-business hours (take time zone into consideration).
How should I tell my boss that I won't be available without sounding confrontational?
I always find difficult to answer such questions when it is unclear what kind of friendliness is between you and boss, and whether boss is Big Boss or a middle manager in the chain of command.
You have two options here: since the first sounded like a joke, you may still want to avoid speaking about the matter and hope the day of vacation arrives. Unfortunately, your boss may remember one day earlier and ask you for a serious meeting.
If you have good suspect that the boss is serious, you should talk to him seriously but not confrontational. Book a meeting with him. I was thinking about this line. Rather than using the line itself, consider the meaning of my statements described later.
Boss, I wanted to discuss again about my vacation. It is my understanding that you need all personnel available in case of emergencies, right? I understand that the we are running a busy time, but I kindly ask you to consider that I need to
cut off to be healthy and productive. I was really waiting for this vacation from long, and I have planned a lot of things to do in Sokovia keeping me busy all the time. Let me instruct someone about my tasks so he/she can back me up!
Analysing the statements:
- I understand the we are busy: since you are percieving the company's situation, you look as part of the team
- Healthy and productive: you are just using a trick to claim that vacation is a benefit for the company, not just yourself
- A lot of things to do abroad: your boss doesn't know if you will be driving the entire Route 66 non stop of spend alcoholic nights at the Ministry of Sound, but I suggest to say something like this to remember that you will be focused on other tasks
- Back up: this is meant to be proactive
For the rest, it's all your choice if you want to be available