Taking long vacations (more than say 10 days) is probably out of the question for solo doctors -- at least, in small towns. The other doctors in the area are pretty much overwhelmed, and don't appreciate adding my business to their already more than adequate load.
I am lucky, living in Oregon, that Nurse Practitioners can work unsupervised in a small office setting, and luckier that I have two acquaintances that have been small-town, rural NP's for a very long time, and even luckier that they are willing to cover the office now and then for short breaks at a price I can afford.
Still, taking 3 months off (I want to go to Australia by ship, train, bus and small boat, for example) remains a dream.
Even when I'm away, I stay somewhat in touch -- but I don't offer to be instantly available.
I have pretty much been on call 24/7/365 since 1975, including about 30 years of a busy OB practice. I have backed off a lot in recent years -- no OB, and the local hospital has hired "hospitalists". But that is life in the solo lane -- you are your practice in this business, and people want to talk about their hemorrhoids and sore backs and Mom's problems when you see them on the street or in the store.
Most doctors these days don't really want that kind of commitment to practice, so far as I can tell. Lifestyle is more important. No one wants my job -- when I leave practice, it's over. On the other hand, that's what the patients want, and increasingly can't get.