It should have one. It should have a big one. And it should be in the prop flow.
The big killer was/is not only that it doesnt have stabilizer, the thrust from the pusher engine/prop is WAY above the center of gravity and the thrust is fairly strong to boot.
So, what this means is that if you ever enter a low or zero G condition (like say a strong downdraft) even briefly, you flip over fowards in the nearly the blink of an eye. In a gyro that is virtually aways fatal. AFAIK only one foward flip has not been fatal in whole history of gyros. Most gyro fatalities have been forward flips. Which tells you plenty of gyros over the decades have been poorly designed.
A gyro with an inline thrust and a good stabilizier CANT do that.
Oh and the big cabin on the RAF doesnt help any either. The air drag on the cabin is also trying to flip the craft upside down or backwards.
If a good gyro is as stable as low slung 4 wheeled gocart, a stock RAF is more like a unicycle that kills you if you ever frack up (or even if you dont).
Note, I am not a pilot or gyro designer, but I have literally spent thousands of hours reading about and understanding these contraptions. I’ve also read, often more than once, every accident/incident report the FAA has on these things, and plenty more from other sources as well.