I always assumed Khamul was off trying to lay the smackdown on Lorien...
But, I do believe Khamul would have taken over with the death of the Wiki (bless him). In any case, Gothmog is only mentioned at this one point. I am unsure (being at work, and without the books), and so I think he probably died at Pelennor. If this is the case, he is not a Nazgul, as I recall (mistakingly?) that the other eight Nazgul were with Sauron when he fell.
Now, Gothmog is seen whipping Easterlings into a frenzy upon the Wiki's death. From what I recall, probably mistakingly, Easterlings have no great love of orcs. So why would they listen to an orc commander? If not a Nazgul, he must be a man, to me.