I have this problem.
I have got used to glancing at the dash when directly under streetlamps in order to gauge speed, etc. This can be a worry when being followed by the law.
I intend to get this sorted soon, fortunately I am a dab-hand with a multimeter.
I would check 12V on the back of the bulb, and at the switch.
If there is, try powering the bulbs with a separate 12V (I.e a big duracell battery) and see if they work themselves.
If the bulbs don't work - new bulbs, if they do but there is no voltage, check for continuity both to the source, and to ground.
Meters are excellent tools once you have got used to them.