I’ve heard witchball as often as disco ball.
I’ve heard that the mirrored balls seen as ornaments in gardens are known as “murgatroyds,” as in “Heavens to.” Maybe that’s it?
My mom says she thinks it may start with a “g”
That ties in with a name for it that I can’t (and couldn’t) recall that had me thinking it was something like gravure or rotogravure or photogravure, none of which has anything to do with a ball.
See if Mom has any other sound-like words we can try to match.
Just in case this thread hasn’t had enough tangents, try http://kol.coldfront.net/thekolwiki/index.php/Disco_ball 
That’s just the German word for “ball”.
I was going to suggest tacky, but since the OP’s mom thinks it started with the letter “g”, how about garish?
Kaleidosphere? Doesn’t start with ‘g’, but ‘k’ is pretty close.
galaball
The thread I started in GQ back in 07-03-2003, 08:32 AM What’s the real name of a “disco ball”? didn’t get any further than this thread has, but I wanted to include a reference to it, so I wouldn’t have to go any further than this thread the next time I see that the topic has come up again. If you can’t tell, I’m really curious to know the answer. I feel there must be one.
Ok, she says this is on the right track, since she keeps getting the word “daguerreotype” stuck in her head when she tries to remember though she knows that isn’t right at all. She says she thinks the word sounded German.
And she thinks it was the common term in the '20s
I’ve only heard “witchball” as referring to the spherical mirrored balls put in gardens as ornaments/bird repellents. Witchballs are not faceted. Disco balls are.
Such is my knowlege.
Drink of it and be whole.
Along the same lines, the German word is “diskokugel.” Does it sound similar to that?
Apparently the first “cite” of the disco ball is in the 1927 German film Berlin: Die Sinfonie der Großstadt (which translates, prosaically enough, to “Berlin: The Symphony of the Big City”). Could someone from America have seen the film and subsequently referred to the spheres as “Großstadt balls” or “Grossstadters”?
Since some of the first places these appeared were German ballrooms, I wonder if people originally used the german word for mirror ball: Spiegelkugel. Spiegelkugel – Wikipedia
Just a thought.