In the morning before starting the car, turn on the headlights for 30 secs then turn off.
Use a cheap multimeter set to DC Volts and check battery voltage, should be around 12.6 volts.
Start the car and hook up the multimeter to the battery again with the car running, it should be around 14 volts.
Then, hold one lead from the positive on the battery to the positive on the alternator, you should have as close to 0 Volts as possible, then touch the neg terminal on the battery to the alternator housing and again as close to 0 Volts as possible.
You are checking Vd (voltage drops) this way to see if your wiring is good on the alternator and battery. If, for example, you read 3 volts on the negative side, you have a 3 volt "voltage drop" which would mean a bad ground or faulty wiring.
Check your fuses that relate to the dash, have a friend watch the dash as you shake the wiring harness to find broken wires if the dash flickers. Don't yank too hard, just playfully shake the harness.
If all of this is fine you may just be having trouble with your PCM. Bad dirty connection from water over the years etc...
Electrical problems require a lot of hunting to find, keep it up, you are lucky the car runs so at least you have time to find the problem.