I’m still a Senator, and I don’t have to be present for the Senate to have the minimum number to begin work, but is my seat just not filled while I’m at my governorship?
The Roman senate did not have "seats," in that it was not a representative body. Nor did it have a fixed number of members. Indeed the senate was neither legally, nor in the general rhetoric of the state, understood as a governing body. To the extent that the Romans understood the concept of occupying administrative and governing "seats," it was in the form of elected magistracies, which were explicitly distinct from the senate. It was an all-important feature of Roman law and of Roman state rhetoric that senators were privati, private citizens. As such if they chose to run for (further, after the de facto requirement of the quaestorship as a barrier for entry into the senate) elected magistracy and won they simply ceased to be private citizens during their year of office. Likewise promagistracies. When one resumed being a private citizen, after the expiry of office, one also resumed being a senator.