There are more then a few sources which depict two-headed humanoids (such as ettins) having more control over some limbs than others – the left head uses the left arm to punch the right head, and such. If an Ettin was to lose one head, would it lose control of the arms that were primarily controlled by that head?

To put it another way: Let’s say the ettin’s left head controls the left leg and arm, and the right head controls the right leg and arm. The two normally work in tandem to function. However, let’s now say the left head is decapitated. Would the right head lose control of the left arm and leg? Or would it “inherit” control of those limbs from the left head, resulting in the Ettin still be able to function fully? I mean, I’d assume both heads share the same nervous system to some extent, but would the left head’s nervous system extend to use both arms when one head dies?