Dunno, John. If it is just a "simple" circuit, there's an oil pressure switch. But if it is hooked up with a pressure gauge and a sender, that's a variable resistor. Given that and the two unknowns (the bulb and buzzer)...the relay allows it to be treated with blissful ignorance.
In either case--if the bulb has near-zero resistance, as most panel bulbs do, it will act exactly the same way as a plain wire, effectively shorting out the terminals of the buzzer that is in parallel with it. That dead short ensures that the buzzer will never work (until the bulb burns out) because there is near-zero current available to it, regardless of the voltage. No?
He has a light, which means he doesn't have (better not have) a variable resistor type of sender. With oil pressure it should be open (infinite reistance) and without pressure it should be a dead short to ground.
Like I said before, if the light bulb remains at or near zero resistance and acted like a plain wire, the fuse would blow. At .5 ohms and 12 volts you'd have a 24 amp 288 watt warning light.
The bulb only has near zero resistance when unlit. The whole inductive resistance thing is difficult to explain, and even harder to grasp. The concept is the same as with an electromagnet. If you take plain wire with a fuse in line, and touch one end to power and the other to ground the fuse will blow. Take the same wire and wind it tightly into a coil, and you get an electromagnet and the fuse doesn't blow. That's because in a wound wire you get a certain amount of inductive resistance when current flows. An ohm meter doesn't supply enough current to cause this, so you read whatever resistance the wire has if it were straight.
When dealing with inductors and light bulbs, you have to look at the power (watts) output. In this case we would have about 3 watts. If the light bulb is wired in series, the total amount of power available for the whole circuit is 3 watts. Enough for the bulb, but nothing else. A friend of mine showed me a great example of this many years ago. He was a part time TV repair man. When working on a TV that pops the fuse in the power supply, he would plug the TV into a special outlet that he made with a light bulb socket in series. He could limit the total power consumption of the TV with the wattage of bulb he put in the socket. A 100 watt bulb would power a 25 inch TV enough to get a picture about half the normal size right in the middle of the screen. It didn't have enough power to stretch the picture all the way to the edge. Same thing in here, except the wattage available is so low, the buzzer does nothing.