[Chad Hauris]

The Zenith models which had an lighted dial usually used a 28 volt bulb which recieves power through a dropping resistor from the 120 volt AC line.
I have retrofitted those which were not originally designed to be lighted with some neon bulbs and resistors mounted on a terminal strip behind the dial.

Usually the only tube problems in these I have seen are the FM converter tube (12DT8)
If it works well the tubes should be fine, they do not degrade just sitting around unused (whereas capacitors do).

To my knowledge none of the Zenith tube type table radios ever had a light in the pointer itself. Some GE's had a lamp which tracked behind the pointer though.

As Tom says a new silicon diode (1n4007) would be good plus a fuse in the power line. Some of the later Zeniths already upgraded to the silicon diode. I would go ahead and replace the electrolytics and any paper caps if present while I had the set apart...that way you won't have to worry about its performance for a long time. Be careful as the power line connects directly to the chassis.