Dang, Boomersway, nice!
Call a couple of my Doctor's office and get a list of office hours and an emergency number. Not sure who you get; with dentist, it is one of the Dental Techs or the Doc. I've used only one, once - and it was my wife (I was too incapacitated and at the ER). Down south, in one hospital, it's a "dispatcher" and they pass it on. You get a call back, the Doc, or his nurse, or the Doc who has the weekend-on-call duty. Virginia Mason excels in communication, I hear Swedish does too, and both have satellite hospitals and Clinics all over the area, up to 2-3 hours away. Big hospitals often have more than one doc in a given specialty, and a biography, list of education, list of sub-specialty, up on the website.
I judge a doctor or facility by the communications and access, these days, too, along with everything else.
Hell, our vet has that deal - but extra charge for evening, and extra-plus for after midnight. Dog bit a porcupine, over 100 quills. We got the evening rate by driving 90 mph (55 zone) and beating midnight. Not sure any human Doc does that, but maybe. To get a urologist like yours, you have a good one - and maybe a silver tongue! To get a local urologist here, the ER has to call him. There's only one, rest are 3-4 hour drive, or almost $1,200 round trip flight, 3 hours one way.