Hi Tim / Chris,
I am no expert in tubes like this but I do know that Ediswan was very big in making Telephone Line Protectors after they merged with Siemens to form Associated Electrical Industries. Siemens set the original design but their name was dropped in favour of Ediswan after being known as Sieswan for a few years.
Very similar looking tubes, but having two electrodes instead, were wired across the two terminals of a telephone line. In the even of a fault at the telephone exchange which was common in the old days, the 240V mains could accidentally be sent down the cables to someone's house which would fry their telephone equipment (British Standard phone lines work at 48-50V DC normally). The idea was that connecting a gasfilled tube across the line would result in the gas breaking down at around 75V thus protecting the telephone equipment. Also people who had mains powered phones in their houses (like for powering a speaker, extra bell etc) were prone to their equipment failing and them sending the mains back up the phone line to the exchange, killing the exchange's equipment. Again in this instance, the gasfilled tube would flash over and protect the line. Usually they'd only arc for a fraction of a second, allowing a momentary high current flow which would trip out a fuse at the exchange before further damage could be done. Such tubes were usually filled with a neon-argon or neon-xenon mixture.
Telephone line protectors became much smaller in the 1960's, and these days they take the form of very small gasfilled spark gap tubes just a few mm long which are soldered into the main line box in each house. They are no longer produced by any of the lamp manufacturers as far as I am aware.
Perhaps your triple electrode tube was some space-saving special used at the exchange to protect two lines, I really don't know but its construction is very similar to the single format tubes!
Best regards!
James.