We've seen madness manifest differently in many of the Asha'man in the course of the series. The first one we saw the taint madness take effect "on screen" (I think it was the first case we saw) was with Fedwin Morr, whose mind was reduced to that of a child. While he wasn't raving mad and psychotic, he was still dangerous as he could still channel but without the faculties needed to know when to stop or why.

Then there was Naeff, who saw Myrdraal in every shadow. However, he was able to function normally despite his hallucinations.

I think Taim is a functional psychopath. His madness is more subtle and that much more sinister because of it. I think it's his ego that kept the taint at bay most of his life. Of course this was when he was alone. Who knows how deep his descent into madness is now that he is in control of basically the male Dreadlords. This is all conjecture, for all we know he can be under the protection of the DO himself.