Electrical problem?

We have been having a problem with the electrical system in the car. The first symptom was the instrument panel would go dead, the turn signals wouldn't work, no gauges etc. Then the battery light would come on for a little while then the seatbelt light would flash on then everything would start working again. No bulbs are burned out. My husband has taken the whole thing apart and can find nothing. (He’s pretty mechanically inclined) We are completely stumped. The only clue we have is that when you put the car in reverse there are no back up lights and the battery light gets brighter. We have taken a voltmeter to all of the wires in the steering column. Any clues?