One possibility is that the affect is in the motor control of the hands, specifically the right hand, which is impeding his ability to actively sign. The other is that the injury affected his ability to generate coherent language.
Work Step by Step
The cerebellum deals with both motor function and language processing, so either possibility is valid. You could test this by testing other motor functions, the use of the hands for purposes other than signing, and/or by having him communicate using language in another way. For example, you could have him speak.