My Case 480C is the same way. Basically, it has a torque converter in place of a clutch in front of a manual 4 spd. trans., so putting the shuttle shift in neutral, would be like depressing the clutch, so as to shift gears on the manual transmission. I would think it would be the same on the Ford, but not positive. Even at that, you need to be at a complete stop, so as not to rake gears.
Mine has a non functional "clutch cut out" switch on it, but it's activated when you touch a brake pedal, like when loading a truck, to raise the bucket, then continue on when high enough. Not designed, that I know of, to shift the main manual transmission. Seems I remember one of the newer Ford hoes we had, had a similar clutch cut out on it, but you had to depress a red button on top of the loader control lever. But again, I believe it was just to stop motion, not for shifting gears.
To my knowledge, the only one's I know of that can be shifted on the go, is the newer equipment, with like a 3 spd. electronic shift on the shuttle lever. My neighbor has a JD 410 hoe, with that system. Pretty sweet if your shuttling material out of a pile, to different areas. But that is a whole different animal, and doesn't have a manual main transmission.