Was surfing ref60.com and found:
Ref60 has an article on the subject of
60 Seconds on Officiating: Movement in the Saddle / Slot.
The take home message is pretty good advice: it's what I do and it works for me.
"Recommended first movement is a slight step back towards the sideline, which gives the center official better depth. The next movement is deciding to dive down one step (or two), or draw back based on your preferred angle of vision."
Since most people start with 2-man, and often have to learn "how deep to be as T", the same learning curve applies to working the C: how to move will improve with experience.