I think that when Rand had suspicions that Taim was holding back from holding his full strength after being ordered to do so, it had to do with Taim's access to the TP.

But...I'm still not sure if Taim is an independent evil working for the Dark One, the student of a Forsaken or a male channeler who was perverted into becoming the DO's pawn by access to the TP (which could protect him from the taint). After all, we know that for all intents and purposes, an Aes Sedai is more than a match for most male channelers in pure fighting ability, yet there are reasons that they have a tradition to put their full strength into a Shield. Part of this reason might be that the TP used to taint saidin might have given the DO access to male channelers which could be used to turn them to the Dark side without using 13 Myrdraal and 13 channelers.

Taim's own personality is extremely disciplined and calculating, and this could add to the impression of menace he projects.