Did the SGC and the Gateroom operate 24/7? Or on a Monday through Friday, 9-5 schedule?
I presume they had to have a night shift and a night command structure in case of incoming signals, or the need to use the gate in the middle of the night or weekends.
Occasionally we see people other than Walter at the controls, so I presume that does happen, but do the SG teams and General Hammond have to be available 24/7??
The sheer stress level and adrenaline flow must force even the greatest of people to need a nice long vacation or even alternating times in service.
Since Teal'c spends most of his time at the Mountain and doesn't spend all his spare time in Kel'norim, he surely would be a good candidate to command the Gate Room during off hours.