prefer that email be utilized for an appointment request what would be a "rule of thumb" as far as response time to the email request.  And, if it was the first time seeing that person would the response time be longer since references would need to be checked.  Just curious as I sent a request to an indie last Friday requesting an appointment for today (Tuesday) and have yet to see a response.

You need to give indies more lead time. Unless they use a service they do all their own admin...and it can be suprisingly time consuming. Additionally an indie may not be able to communicate back to you under certain circumstances. For example MJ tragically lost her grandmother and is back up in Canada this week. I seriously doubt she's checking emails.

With an agency you'll get a quicker response for two reasons. 1st they have a dedicated admin function of some kind to support the gals. 2nd they usually have other options even if the gal you sought is unavailable which they will try and communicate (read sell) to you.

I usually allow two weeks lead time for an indie and 3 days for an agency.

In the past, I've contacted both indies and agencies asking them to pre-screen me before I was able to suggest a date and time, thus it is only a question of schedules when the time comes.  I have found some indies and agencies willing to do so, give it a try.