If you are trying to meet on the same day, then I usually allow for 4 hours max. If I am moving on to find someone else, out of courtesy I let the guy know of my plan to move on. I often try to schedule a meeting for the following day, or the following weekend, and have scheduled a month or two in advance.
The "Available" on RM, I consider it that the response could take hours because the guy could be eating, busy with a client, but hoping to see another one the same day, what have you... Now, if their "name" is green, meaning they are "online", I usually expect the response within an hour or two. At least that's what I have experienced... Sometimes, I think they are trying to schedule their time or they are trying to resolve conflicts when clients are rescheduling... Hope this helps.