Every "emergency engine" I ever saw in a telephone building was a conventional diesel engine. My father-in-law was shop foreman for a company that sold and service large earth moving equipment in Enid, Oklahoma, and from time to time they were called upon to routine the auto-start emergency engine in the Enid c.o. It was a conventional GM diesel engine like those used on earth moving equipment and locomotives.
Offices with 24-hour coverage had larger diesel engines that were started manually. Both auto-start engines and those started manually were tested once a week by pulling the commercial power and making sure that the officde transferred properly to the emergency engine and, in the case of auto-start engines, that it started properly.
As Lisa says, the batteries would carry the load for some time. The batteries always carried the load, with commercial power or emergency power being used to float the batteries and charge them continuosly.
Usually the emergency engines, at least in offices with manual start, were tested at 7 a.m. on Wednesdays and run for an hour carrying the load. If you happened to hit dial tone or ringing tone at that time, you could hear a slight blip in the tone as the load shifted from the usual ringing machine running on commercial power to the backup which ran from the c.o. batteries.
C.O. batteries were very large compared to the usual auto battery you think of, and existed in large numbers.
As to Servel refrigerators, the patents (and perhaps the name) were purchased by ArkLa Gas (originally Arkansas-Louisiana Gas Company). It his now combined with another large gas utility and has a double name.
Wes Leatherock firstname.lastname@example.org email@example.com