What a terrific find!
Mom's has this mystery item inside as well. We didn't use it for anything - happy to hear of its possible use as an ink well or needle spot.
Her Singer was the model 201, & I believe that cabinet was sold just for a couple Singers - 201 & 15-90. The cabinet now resides in my basement, but the gem of a machine was replaced by Mom many years ago when she thought she needed something with a zigzag option. Wish I could find a 201 to put back into it.
I plan to restore the cabinet this summer; seems my brother used it for a table in his laundry room - bleach, detergent, etc & returned it to me recently in terrible condition.
I hope elbow grease will make it the beauty I remember as a child.