Antother thing you can do for dial light is to use one of the Chinese ( of course... )  “pencell flashlight bulb” replacements.
These use an LED but include in the same size bulb package, a small relaxation oscillator to boost the 1.5 volt supply source

to the ~2 volts the LED wants. You can actually force fit and bend flanges on the original dial light holder to hold such item,

or you can solder it in. Richard Brunner found that you actually do NOT hear any spurious from the LED voltage boost circuit.

This too works pretty well, and is pretty easy to implement. A lighted radio dial is part of the magic.

-Hue Miller