Has there ever been a Automatic generated 'Happy Birthday'
message we can send to classmates by a toggle box etc.?

Apologies in advance as I have not been on the forums in some time and I am revisiting an old topic.

Yes and then No. It was going to be done (2009) and then there was concern about "spam" issues (2014) and so forth.

Most of us desire an automated custom message option. What do we know

Closest you can get is the What's New generated birthday post (and the home page list).

FaceBook sends out like this:

Topic "Today is Some Person's birthday"
Content "Wish Some Person a happy birthday"

So obviously that's not a problem for them

Search using "automatic birthdays" on the top of this forum to see discussions from "on the list" to "not going to happen".