I have to assume you're trying to either be sarcastic or trying to make some point that eludes me. The language is really pretty clear for anyone with grade school education. This being a generation gap thing is insulting to both the younger and older generations. Just being dim isn't something that should be blamed on age.
If when = "at what time", then you can't say "Let me know when works for you" because you can't say "Let me know at what time works for you". By saying "when works for you", you're trying to use "when" as a noun phrase. But "when" is not a noun, "time" is.
Would you also use "how" in this way? "Let me know how works for you" instead of "Let me know what way works for you"?
In my 40+ years of speaking English, I've never heard this phrase used this way. Call me kooky. And I've been through a very nice set of elementary, secondary, and undergraduate schools.
Maybe it's the "works for you" that throws off my grammar sense.
I'm also a native English speaker, and I also presumed that a word had been omitted in the title. It was easy enough to figure out from context once in the article, but from the title alone I didn't even try to guess.
from:
http://en.wiktionary.org/wiki/when
when At what time. They were told when to sleep.