[JLMounce]

It may be possible to replace the lights in the instrument panel without taking the dash panel out of the car. When doing this, you may want to continue to use halogen lights because they don't require specific mounting directions for polarity. LED's typically must be installed in a specific orientation to work correctly. In the context of installing these on your back, under the dash, that can be problematic.

If you get to the point where you believe you need to remove the dash panel to get where you want, you may wish to budget for a replacement. The plastic in your panel is 60 years old and brittle. There's a fairly high likelihood that while taking the panel out, disassembling and re-installing that mounting tabs can be broken. If it comes to that, the repops tend to be of adequate fit and quality for anything other than a concours level show car.

I agree on the PlastiX polish, but do yourself a solid and grab a foam rotory pad for your electric screwdriver. It's gonna do a lot better job than trying to get in there with your hands and a microfiber. If you need some basic touch-up on the chrome edges, get a chrome paint pen off amazon. These do a surprisingly good job at evening out any areas that the vacuum chrome has pealed, or yellowed. Good enough for a daily driver, without the expense of vacuum chroming the dash again.