This is just a guess, but the pilot lamp is probably a Type 47 or equivalent 6.3 V/150 mA bulb.
If you have the ballast tube, and it is good, you can figure out the pinout with a high-resolution ohmmeter (filament will only be a few tenths of an ohm when cold). The highest ohms reading will give the end terminals, and the lowest reading between these two pins and the third active pin will indicate the tap pin (and also the orientation to the "low side" of the filament), the tap being asymmetrical.
Are all of the tubes the correct numbers for this set?
It requires 300mA heater-string tubes.
This ballast tube is an oddball, and appears to have been used in a very small number of sets. Wouldn't surprise me if it had been changed out for a more common tube long ago... is the number printed on the tube correct for the set?
Absence, or wrong current rating of the dial light may affect operation.
The schematic shows a ballast tube of 878/R48 and that is what is on the tube that is in the radio. Looking from the bottom of the ballast tube and starting with the first large pin as number 1 and numbering clockwise I got these readings; 1-2 open, 1-3 733 ohms, 1-4 71 ohms, 2-3 open, 3-4 660 ohms, and 2-4 open. No readings were a few tenths of an ohm cold. Seems it is a bad tube. and ,yes the dial light works. Next thing is what resistor could I use in the filament string?
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Hang on, the ballast tube might not be bad. Apparently I don't understand its operating principle. My thinking was that it was like an incandescent lamp where resistance increases as the filament heats up. But your ohms readings don't support that. In fact, when hot, the ohms would have to be a fraction of what you were reading in order for the set to operate.
Be that as it may, the ballast tube can be replaced with two resistors in series that together absorb 45 volts from the series string (leaving 80 volts for the tubes). This assumes a line voltage of 125V.
The "Top" resistor would need to absorb 39 volts (45-6) and the "bottom" resistor, 6V. The heater string needs 0.3 amps. So, to drop 39 volts at 0.3 amps would require a 130 ohm resistor. This would need to be a 20 watt resistor (derated for reliability).
The "bottom" resistor needs to drop 6V at 150 ma, which calls for 40 ohms. This is the equivalent resistance of a Type 47 dial lamp. When the lamp is wired in parallel with the resistor, they together
pass 0.3 amp of current. This can be a much lower-power resistor- 2 watts should be fine (also derated).
If you want to forgo the dial lamp, a single 150 ohm 25 watt resistor can be used.