Hi
mrsD let me know of your post.
My son is now in his 20s but has TS, genetic, and diagnosed when he was 10. Your doctor may be correct in ruling out TS as that usually does manifest with both verbal and motor tics.

I must say I have never heard of what your neurologist has described though? and really feel for a young child being on a strong drug like Neurontin??

Does your child have a history of strep infections or has he ever had a tick bite that you are aware of? Conditions triggered by those can manifest with tics.
I have more info if you require it.

Even things like allergies (food and environmental) can trigger tics, and I also know of some people who have developed tics due to misalignment of the TMJ jaw region, photosensitivity and a whole bunch of other factors