Tom MacWood,
On the first page of your copy of the book, "The Garden City Golf Club, a History", what appears on that page in your book ?
The back tee you reference on # 13 is not a tee.
In fact, it has trees growing in front of it, blocking the view and flight of anything headed south, like a tee shot.
And the walking paths you allude to are roads, vehicular paths if you will. The same markings can be seen on the 12th hole.
In addition, roads traversed the club's property until fairly recently, and they can still be clearly seen on many holes today. At one time, thirteen holes had roads crossing the lines of play, and one hole, # 9 had two roads, and possibly three roads crossing the lines of play.
You might want to turn to the fifth page, in the section entitled, "The Golf Course" and look at the old schematic of the entire 18 hole golf course. You will note that there is not more then one tee per hole on that schematic.
If you want to, I'm sure that you can find a way to have your 1950's schematic posted, both TEPaul and I are seriously interested in it.