This demonstrates the way the speed change operation should work. (I've lifted the turntable off for the demonstration).
Over time the belts on these forty year-old machines perish and stretch making the turntable run slower and at an inconsistent speed.. You can get replacements for them, but they have to be the correct belt. Best buy two, I've a spare sitting in the tray. But you should get about twenty years wear out of 'em.