That makes sense, but I think the vast majority of tools that need time values would actually expect users to just input a string and parse that themselves.

IMO anything other than the basic types supported by JSON (number, true, false, null) ought to be be parsed as a string. Or if you really insist, some kind of special syntax to make it clear it's not a string would probably be acceptable.

What do you mean by "support"?

Does anyone do it that way?