When did you move to Montreal? My late uncle, in the 1960s and 70s, had a house in Lachine which had a wing which was his office.
We moved here in fall, 1968. We got a new GP with an office near us (TMR) but not near where he lived in 1980.
To the extent this is a tradition in Australia I suspect it might be a Melbourne tradition. I’m not sure I have seen anyone from Sydney chiming in yet.
Certainly I’d never heard of this before, or seen it, in Queensland. It fits with Melbourne being a somewhat more olde world place with traditions closer to England.
Yes - seen in Sydney. Two of my four local doctors working from their own premises have them.
I’ve never heard of this “doctor’s red light” thing, but wouldn’t it make it readier to hide blood?
:: looks down at red shirt I am required to wear at work ::
Uh-oh
I hope you don’t work on a starship!
“You’ve got red on you.”
As a complete and total aside - when food scientists run taste tests, the testing is done in a room with red light. This prevents tasters from taking cues from the look of the different foods.
I have heard two different explanations for “red light district”.
And I heard them both on History Channel documentaries. 
Claim #1: When leaving a railroad station, conductors would carry a red signal lantern. If there were an emergency, and the conductor needed to be contacted, his co-workers would look for the red lantern. Railroad conductors were well-traveled, and wise in the ways of the world. If you wanted to know the best restaurant in town, look for a red lantern in the window. If you wanted to know the best tailor in town, look for a red lantern in the window. If you wanted to know the best brothel in town, . . . .
Claim #2: In World War One, in German-occupied Belgium, enlisted men’s brothels lit their signs with red lights. Officers’ brothels lit their signs with blue lights. When entering the red-light district, men had to submit to a “short-arm” inspection to check for STIs. Officers, being aristocrats, were expected to police themselves. Consequently, the blue-light districts were rife with disease, while the red-light districts were much safer.
My personal theory #3: In the days of yore, respectable businesses would close early, and respectable districts would be lit only with white streetlights. Late at night, red neon lights indicated businesses that catered to less respectable customers, such as bars, theaters, and brothels.