Bill,
if you look at the 1919 and 1950 timetables, between Antonito and Chama Telegraphones were located at
Antonito (presumably the station)
Lava (booth - siding until 1955)
Big Horn (booth)
Sublette (in the section house I think)
Toltec (hanging box)
MP 311.3 (booth - near Mud Tunnel)
MP 315.4 (booth - between the site of Toltec Section House and Toltec Tunnel)
Osier (station)
MP 323.0 (booth - old Los Pinos siding)
MP 328.0 (booth - near Apache Canyon road)
Cumbres (station - section house after 1954)
MP 333.0 (booth - Coxo area)
Cresco (booth)
Chama (presumably the station)
If you plot the various lineside structures (stations, section camps, booths, etc.) on a map of the railroad and the telegraph line, you'll notice that telegraphone booths got installed (a) where a siding but no station or section house existed, and (b) where the telegraph line separated from the track for a significant distance.
Lava - siding, no station
Big Horn - siding, no station
Toltec (box) - siding, no station
The booths at MP 311.3 and MP 315.4 marked where the telegraph line dropped into the valley of Toltec Creek, bypassing the Toltec section house.
The booths at MP 323 and 328 marked where the line took a shortcut across the Los Pinos valley, bypassing the Los Pinos section house.
The booth at MP 333 marked where the line rejoined the tracks after a shortcut down the hill from Cumbres.
Cresco - siding, no station.
The purpose of the "siding" booths is clear - a "substitute station." The "shortcut" booths may have served as locations to test for problems that couldn't be seen from the roadbed (saving the wire man a long walk over rough terrain), as well as allowing isolated section houses telephone access (walk down the tracks to the nearest booth).
I'd be interested to hear from Mr. Trump on my speculation.
JAC