I would expect 11 1/2 volts to be sufficient for a 12v light bulb. Can you pull the bulb and socket out of the dash, run a jumper wire to ground, if necessary and observe the operation of the bulb? If it is bright, then you know the bulb and socket is working correctly. If it is dim, see how much voltage is at the socket to rule out problems there and test the bulb with known good wiring and a 12v power source. If those check out good, then there must be something in the panel blocking the light, dust, dead insect, spider egg sack, etc.
A standard bulb should work fine. You have to be careful with LEDs as they project light in a relatively narrow angle, directly in front whereas a bulb can illuminate, say 270 degrees, it depends on the design, but a much wider range. As a result, LEDs don't always work well when used in places that were never designed for them. And, of course if your problem has nothing to do with the electric portion of the lighting, then an LED will not do a thing.
Lawrenceville, GA