David Simon’s acclaimed TV show The Wire used “out of pocket” in the OP’s second sense quite a few times. It was generally used in regard to a witness or a suspect that they couldn’t locate at the time. Along the lines of, “He’s out of pocket, and we need to locate him.”
Damn. I’ve watched that series, and the phrase has somehow not registered with me.
The online OED records the “unavailable” sense, notes that it’s a US usage, traces it back to the O. Henry cite from 1908, and suggests that it invokes “pocket” in the same sense as in phrases like “in his pocket” meaning under his control or influence, assured, guaranteed; and “to pocket something” meaning to keep something to oneself, to keep control of something.
So to say that someone is out of pocket in this sense is to say more than that they are not at work; it implies that they can’t be reached or communicated with; that they are not subject to direction or control.
You probably haven’t watched it, oh, about ten times like I have. 
Found a bunch of examples in the first two seasons alone:
Season 1, Episode 3
Daniels: Everyone else roll out?
Kima: You were upstairs and out of pocket, so I cut them loose.
Season 1, Episode 12
McNulty: All the work we did to get up on this fucking wire.
***Freamon: *** You don’t hit these guys the way that we did and expect them to stay in the pocket.
…
Trooper Reese (on phone):*** Grandmother says this kid’s been gone two days.
***Daniels (to Carver): *** Wallace is out of pocket.
Season 2, Episode 11
Stringer (to Omar): Stinkum? I mean, you closed the book on that nigger your damn self. Avon, he out of pocket for the time being
Season 2, Episode 12
***Daniels: *** We left the man we think is the number two for the operation on the street, hoping he’d lead us to number one.
***Rawls: *** We have people on him?
Daniels: He’s out of pocket at the moment.
That seems to give a clue about how the usage may have originated, since this one looks pretty clearly like a snooker/pool metaphor
Hah! Must have just gone over my head as street talk and not made an impression, obviously.
If it makes you feel any better, I didn’t pick up on that phrase in The Wire either, though I watched it religiously. On top of that, I grew up about 20 miles outside of Baltimore and was paying a lot of attention to the accents and regionalisms. Oops.
I’m pretty sure I grew up hearing my dad use it to mean unavailable (Southwest Arkansas, 1960s-70s).
Coincidentally, I just saw this in an email for the first time earlier today, and I assumed it had to be some kind of weird autocorrect or voice-to-text issue. I guess it’s something people actually say.
I’ve worked for three Fortune 20 corporations over my career. Over the past 25 years it has become pretty standard to say someone is “out of pocket” to mean they are traveling on business.
“Out of pocket” implies the person has made some outlay of funds (airfare, hotel, meals, etc) for which they will be reimbursed when they submit their expense report. It’s also used if the person is simply traveling across town because they will again submit an expense report for reimbursement for any expenses incurred - mileage, client meals, etc.
“Out of pocket” is generally not used to indicate the person is working from home. In that case they are “working remote”.
When I was younger it used to bother me because it ought to mean the person is on the hook for paying their travel expense, but I got over it as there are so many worse abuses in corporate speak.
West Virginian and never heard it except in terms of financial arrangements.
Damn, that means I and many of my co-workers have been idiots for years! I didn’t know that. Thanks for the update. 
For the OP, I have heard and used that phrase with my co-workers for at least the last 10 years. It just sounds good and efficiently gets the point across. I will be out of touch for a while and not part of the current activity that requires frequent communication. It means that the team I am working on where I give and receive frequent communications will have to do without me. Sometimes that message is received with considerable relief by my co-workers, sometimes they actually miss me. It depends.
Glad to help 
I’ve used “out of pocket” like “I’ll be out of pocket” to mean unavailable for as long as I can remember, and in fact the medical bill usage was a new one to me when I first heard it.
“Out of pocket” expense makes direct sense, so isn’t hard to understand.
I don’t know the origin of “out of pocket” as unavailable.
Worked for the Government (US) for 34 years and heard it used both ways for many years. Definition depended on use; if 'out of pocket" was for something during a trip/TDY that the government wouldn’t pay for, then one; if it meant you’d be away and out of touch for some time, then the other. All dependent on context.
UK perspective here.
I’ve never heard it used in an “unreachable” sense ever.
I would understand it as meaning one of two thing. Either I was financially down, i.e. I had to pay for something I didn’t expect and so was now “out of pocket”. Or that I have to cover the cost of something myself until a third party reimburses me, i.e. “out of pocket expenses”
I started hearing it in the early 1980s. I remember because I remember who I first heard it from. I had the impression at the time that she just misspoke, that she was telling me someone was out… of…, and while trying to finish the phrase, “pocket” blurted out because that word sometimes followed the previous two.
But then I heard it from her more, and from others, who I then considered to be idiots about language. Nowadays it’s so common that I figure it could be considered correct, that people have heard the phrase with the new meaning so much that they’re not even familiar with the old meaning. Bugs the shit out of me, but I realize that prescriptivism is futile.
In the UK I have never heard it to mean “unavailable or unreachable”. But also it seems to me the financial meaning has a slightly different sense over here: “out of pocket” just means that you have lost money. Eg if you sold something on eBay and the buyer claims it never arrived and claims their money back, you would say “I’m £30 out of pocket”, or “That’s left me out of pocket”.
We do also use the phrase “out-of-pocket expenses”, though, to mean your own money spent, which might be claimed back from an employer, say.
… and I just realised Novelty Bobble said essentially exactly the same thing.
We used it all the time in the narcotics investigation world. Specifically, when you couldn’t reach the informant or didn’t know his whereabouts. That said, I would never use the term to refer to myself, only someone else that you normally had some control over.
Exactly the same for me. I’m from the Pacific Northwest part of the USA, and briefly lived in Kansas and also for a couple of years on the island of Guam. It seems to be a regional thing from parts of the South to use it as slang for “unavailable”.
My (completely speculative) assumption is that it refers to something unavailable to you because you don’t have it with you; not in your pocket. But again, I’ve never in my life heard this phrase used in that sense before this thread, and I’ve been a professional for over 20 years working in small business, big business, and government. It’s not a common usage in the professional world, but perhaps in a certain field or region.