My wife'* olds has a poltergeist.

The dome light turns on and off by itself. Walk into the dark garage at night and it is on. Come back later and it is off. She drives the car to work daily and all seems to be fine. Leave it undriven for a few days, like over the weekend, and the battery is dead.....so dead that the keyless remote will not unlock it. The battery is a new Interstate from Costco, replaced for this problem and perhaps didn't need to be but we live in Arizona (notoriously hard on batteries) and the battery was several years old. It will always take a full charge on the charger. The local shop that we use and trust had the car for several days and could never witness a problem. They say the charging system is working fine. Sometime a relay chatters from the panel under the passenger side dash. Does it chatter because the battery is low or could it be the culprit? The car is long since paid for and in great shape.

Any ideas?

Sounds to me like you have a bad relay. Look in the tech info area in testing and you should find a thread called amp draw test. This may help you track down your problem.

I think the clicking relay could be due to the lights being, and it is trying to power the relay and the battery is dead. When you see the light on, is it on for hours at a time, or for 30 seconds or so?

You could try pulling the fuse for the courtesy lights, and let the car sit over the weekend. If the battery isn't dead, then you know the problem is in that circuit somewhere. (Bad relay, door switch, etc.) There is a relay for the interior lights, probably the one that'* clicking. Electrical gremlins are a real pita!