What does "turn down a glass" mean?

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...

And also:

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.

Solution 1:

I found this on reddit...

In memory of a drinking companion who has passed away, it is customary to turn down (= turn upside down) a glass (representing his/hers) on the table the next time you go drinking, and pause a moment to remember him/her. Thus, turn down a glass = stop for a moment of thought.

That's good enough for me, and it certainly makes sense in the first of OP's cited examples. Personally, I suspect the second example (Napoleon Hill, Think and Grow Rich, 1937) may simply be a "misuse", where what Hill meant was that his subject avoided excessive drinking, but I'm not too sure about that.

In case it's not obvious, this isn't a well-known saying. I just searched Google Books for the exact text turn down a glass for, having found nothing with turn down a glass in - expecting ...in memory of [dead friend]. In the event, most of the results on the first page were actually links into Think and Grow Rich (OP's second example) - but as luck would have it, that search also turned up this excellent example for the "in memory" sense...

“Turn down a glass for me,” was the last written message novelist Jacques Futrelle sent from Europe to a friend in Atlanta.