I don't see why etiquette only applies to people in your immediate proximity, when we live in a world of long range communications. If my mother needs to speak with me and calls, why is that immediately undervalued compred to a friend that happens to be near me telling me about their drinking escapades of the night before? Also as a business owner, calls and messages come to me all the time that often require immediate responses. I claim the right to review the queries for my time and prioritize them accordingly, no matter if they are from someone in fromt of me, someone who taps me on the shoulder while im in the middle of a conversation, or even from a buzz on my phone or a tap at my wrist.
I do think it is society that needs to adjust to the fact that we can connect with important people in our life without direct physical proximity. It didn't used to be that way, and now it is.
When people talk about seeing others mindlessly immersed in their phones at restaurants, I think in most cases that is actually a different thing. Passively browsing instagram or facebook or playing angry birds is a totally different thing than responding to a live-person notification. I completely agree it is rude as anything and the fault of the individual, when they choose to remove themselves from the immediate social situation just because they are bored.
I think the distinction between those use cases should be highlighted.
The problem the OP mentions is a real one. People are accustomed to a watch telling you one thing: the time. They are NOT accustomed to the wach trying to get your attention, and so the act of checking it has the insinuation of boredom or anti-social distraction, and hence the reaction. Once people realize that the watch is actively informing people of messages and calls and select emails, I think this reaction will change. It as the same difference as described above... Is the user being queried for their time, or is the user disinterested in their present surroundings. One is rude, the other -- if not strictly polite -- is at least warranted.
Edit: I'm speaking more in general social environments... Obviously there are situations where it is not appropriate to check notifications at all, and the OP's work environment might be one of those situations.
This reminds me of beepers and how people might be "on-call" and clearly they need to be responsive to it. I was the manager on-duty a resort for awhile and the beeper actually played the recorded message out loud. I was apologizing for it constantly.
I have had people call me out for staring at my phone for so long too. And then I just tell them what I'm doing: "I'm reading a book." And then they're confused.
As far as people working in customer service, I think if you are good at what you do people won't feel you're being rude by looking at your watch or phone. If however, they feel like you're being ineffective they may call you out for looking at your device.
I used a device for work when I worked in a store. it was really important to me that my customer understood what I was doing and why. "Let me check inventory for you." "I'm going to be able to do that for you right here with this device." "This is so much faster then when we had to always go back and crawl around in the back room."