Depending on who wired your car up and where they attached the wires on the gauge, one light (usually on the right) is the alternator, while the other (usually on the left) is oil pressure. Someone with the various builder vehicles (Vintage, Beck, IM, etc) should help with this as to which light is which on their respective cars.
Other than both being on the same gauge face, they are totally independent and neither affects the other in operation. If the oil pressure drops, only the oil light will come on. If the charging circuit fails on the alternator (the voltage drops below 11.4 volts and it is no longer charging the battery) the alternator light will come on. If both lights come on you either have the ignition turned on but the engine is not started, you're sitting at idle on a hot day, or in very big trouble.