Check the 12V fuses. There is generally a RED LED indicator light when the fuse is blown. That RED LED indicator light may be supplying enough current to light up the LED bulb in the fixture dimmly, but not enough to illuminate a regular bulb.
The RED 12V indicators on the fuse panel are usually in parallel with the fuse. If the fuse is good, you will get the full 12V and can supply current upto the rating of the fuse. If the fuse is blown, or removed, the circuit will actually still be supplied 12V but only the very small amount going through the RED indicator LED on the fuse panel. This may be around 20mA or so. That's enough to light the LED on the fuse panel, but not enough to fully turn on an LED fixture bulb.
If the fuse blows again when you replace it, you may have a short circuit somewhere.