I got most of the data from L.E. "Ed" Trump. He was employed by the D&RGW as an engineer in their communications department. If you read the other articles, you will find he was also a student fireman on the narrow gauge ! Note that the telegraph circuit was active on the narrow gauge until abandonment. The D&RGW had some live circuits for a few years after that.
Telegraph repeaters used sensitive relays in some rather ingenious circuits. I believe Ed has some evidence that a repeater was located in Durango. I guess the circuit was not quite strong enough to get the rest of the way to Silverton and Farmington.
The problem with the telegraphone is that it used a ground return, which means lots of noise. John Norwood describes yelling into the things, and also the fact that you could hear the telegraph leaking through, which was used by train crews to advance their trains in certain situations.
Note the short article in the Telephone section of the communications instruments pages. In 1938, the telegraphones were replaced with a more modern telephone circuit. The telegraph circuits remained in place.
Chama had a dynamo which powered that end of the telegraph circuit. I have wondered what happened to it, and perhaps it is rotting in the scrap heap behind the roundhouse.