Hi Nelson, I'm guessing the thing that looks like a relay is going to be a vibrator supply, don't know what voltage it would run off maybe 6V or 9V, just a wild guess, wouldn't think it runs from 1.5V but I could be wrong. Looks like there are two small transformers, the one in the center next to the CK1027 is probably a step up transformer for the Geiger tube and the one by the speaker would be the audio output transformer. Couldn't find any data on the RCA 4-45. Miniature wire ended tubes from that era would have heater voltages either 1.25V or sometimes 0.625V so you would wire two heaters in series if running from a 1.5V heater supply.
Many if not most of the miniature wire ended tubes do not have a cathode and would use one end of the filiament. If the tubes have 4 wires they are most likely triodes and the connections would be F-, F+, G and A, where F+ would most likely serve as the cathode, that way the grid would be biased to -0.75V (average heater voltage) assuming 1.5V heater supply. Pentodes would have five wire connections, F-, F+, G1, G2 and A, where G1 is the control grid, G2 is the screen grid and G3 the suppressor grid would be internally connected to either -F or even sometimes +F. Given time I think you will have to trace out all of the wiring to figure out what is going on.
EDIT: I should add that maybe the HT battery could be 45V or 69V and not 90V
Chris