It is certainly worth more than $3. It was made in Sorrento, Italy. I think 1960s or so. If you google Sorrento box you will most likely get antique inlaid wooden boxes, Sorrento ware. Very beautiful, but nothing like this.
I think closer to 1970s or early 80s - look at the screw heads. The 60s ones had old style screws usually. Plus, the clear plastic label. The older ones had goil foil printed ones. Worth $3 any day.
Personally I prefer inlaid wood Sorrento ware, but I am more of an antiques person. Others may find Sorrento ware too flashy. Different strokes. Otherwise the world would be a boring place.
https://www.worthpoint.com/worthopedia/jewelry-box-sorrentino-sr42-music-box-1869094644 similar. sold for $49.
In the 1970s (edit: probably into the 80s, but I stopped going to malls, lol) there was a music box store in every mall (at least where I lived, central Florida)... shelves and shelves of these. I always wanted one, but they were much too expensive for my family.