I do not know your answer, but one starting point would be the employee timetables from the period. If the Salida Division still had a dispatching office at Gunnisson the timetable would probably show Chief Dispatchers at both Salida and Gunnisson. If it shows only a Chief at Salida, it would be logical to assume dispatching duties shifted on or prior to the date of the timetable. My fragmentary collection of timetables does not go back that far, but when the Pueblo Division took over the Alamosa Division it showed Chiefs at both Alamosa and Salida, but that was in the early 50's.
JBWX