Well, at least it is
A voltmeter lol. The cig lighter is connected to a fuse that also supplies power through the headlights switch for the pakring and tailights. So that matches up with your dim lights issue at idle. It might be a regulator but a regulator issue would not likley cause both such a high voltage AND such a low voltage. The fact that you can see 15.5 volts means that the regulator CAN command the alternator to put out a pretty high voltage and the associated current, so that says the VR can do its job.
What is more likely is that you have some siginificant voltage drops in the wiring. This might not seem rational to cause the high voltage you see but here is the reason: The regulator looks at what ever voltage is coming back to it from the ignition swith and harness, and adjusts what it is commanding to the alternator (by adjusting the field current to the alternator, which is what the VR controls). If it sees too high a voltage, it turns the alternator down. If it see to low a voltage, it turns the regulator up to compensate.
It is common in these cars to have excess voltage drops in the wiring as everyone has been discussing and the VR will see too low a voltage; it will then command the alternator to 'turn up'. At higher RPM's, when the alternator can actually do this, you will see excessively high voltage like your 15.5v. At idle, the alternator can't put out such a high voltage, even if the VR is putting all the field current into the alternator that it can; the alternator just can't put out the poop the the VR is 'telling' it to do at low RPM's. So the alternator voltage will be low (normal) and the readings in the rest of the car will be even lower due to the voltage drops we have all been going on about.
A bad VR will most likley fail so as to produce low or high voltage at all RPM's high, all the time, not high and low like you have. You don't seem to want to tackle the wiring and that is understood; it is a lot of work, buuuuut......it is pretty plain that this is the most likley problem and is a very common one. If you can afford a radar detector, you can surely afford a simple voltmeter, which will give you the best tool to tackle this.... costs about the same as a VR.
"Luuuuke....listen to the Force......it wants you to fix the wiring......"