Background:
At my workplace we have a small open office of under 10 staff.
While I work as a developer which includes making & receiving phone calls for technical matters, I sometimes answer the phone for general calls when others aren't available to do so.
Often, callers ask for my manager. When this happens I need to know who is calling, what they want, and if they are a client before I can make a decision about whether to pass along the call (I have instructions about what calls should be passed on and which ones referred to email, and by default they are "not in the office" unless the call is one they are expecting).
Often the caller will avoid divulging the subject of the call and instead ask when the manager will be available, promising to try again later, then promptly hang up.
Rinse & repeat 1-2 hours later when they call again - often it will be me answering the repeat call, I really want to tell them to stop wasting both our time and just tell me what it's about so I can do something!
I also don't gain any brownie points by telling my manager "someone called, don't know what it's about or where they are from, they'll phone back". That's useless to the point that there's no reason to pass it on.
My responsibility here is to pass along anything pertinent (not sales) while handling any technical issues myself. Sometimes divining the actual purpose of the call (and sometimes even the identity of the caller) is very difficult when they are uncooperative and avoid answering your questions.
An example of one of these discussions can go like this:
Me: Good Morning / Afternoon, Company X
Caller: Manager Y please
Me: I'm sorry they're unavailable at the moment. Can I help / take a message?
Caller: When's Manager Y available?
Me: I'm not sure, sorry. What's the call regarding?
Caller: I'll try again later, thanks.
hangs up
Question
What are good strategies for finding out what a call is actually about, when the caller is uncooperative, will only speak to Manager Y and doesn't want to waste time explaining themselves?
Should I mention it if they keep phoning back that they will not be able to speak to Manager Y until I have these details?
Update
After some comments / answers I've spoken to my boss who has basically said what I'm doing is about all I'm expected to do (enquire about the nature of the call, who the caller is, offer to take a message, offer to help). He agrees that it's difficult which makes me feel better if nothing else!