I don't think there are any original vacuum tube computers still running. There are working replicas of the Colossus, ABC, SSEM and (almost complete) EDSAC.
As far as tubes, the 700-series circuit manual [1] shows mostly dual triodes: 6211, 5687, 5965, 6350, 6072, 6528. Also 6136, 6197 pentodes. And probably a variety for special cases (e.g. power supply, core).
There certainly isn't any still running 705 which serves useful purpose. In fact they were probably all replaced by 7080s and then 360s in sixties as 7080 is software compatible and specific 360 models have some support for running 7080 software. Also the software that ran on these machines is probably simple enough that it got rewritten for more modern machines cheaply.
I hadn't heard of Eccles and Jordan before this article; I had previously believed that the flip flop was invented by Eckert and Mauchly. Good to know!
