I was reading Think and Grow Rich by Napoleon Hill (from the early 1930s) when I encountered this strange expression. This is the context of the phrase:
Somewhere, as you read, the secret to which I refer will jump from the page and stand boldly before you, if you are ready for it! When it appears, you will recognize it. Whether you receive the sign in the first or the last chapter, stop for a moment when it presents itself, and TURN DOWN A GLASS, for that occasion will mark the most important turning-point of your life...
We pass now, to Chapter One, and to the story of my very dear friend, who has generously acknowledged having seen the mystic sign, and whose business achievements are evidence enough that he TURNED DOWN A GLASS. As you read his story, and the others, remember that they deal with the important problems of life, such as all men experience.
I will greatly appreciate if someone may clarify its meaning.