This app was mentioned in 2 comments, with an average of 1.00 upvote
Download an auto dial app for your phone. It'll call, and when you get the engaged tone it'll end the call and try again.
I personally use this one, although I doubt it's the best by a long shot
Be careful though, as the one I use sometimes calls them back once I've hung up.
I call the doctors so infrequently that I download it, use it, then uninstall again after use.
It's also worth remembering that if you get a recorded message rather than the line being engaged as such, you'll need to manually end the call for it to redial.
https://play.google.com/store/apps/details?id=cn.menue.superredial
Thats the one I use, but theres quite a few on the appstore.