First, there are chimes or beeper alarms used in cars today that are more pleasant than the raucous buzzers that most carmakers dispensed with many years ago.
Perhaps one of these newer noisemakers could be adapted to this low-pressure warning system and simplify the circuit, while retaining an automatic-check function whenever the ignition is turned on.

Second - A buddy that competes in vintage sportscar racing installed a large low oil-pressure warning light on his steering column to supplement the guage. I think he found his low-pressure warning kit through a racing supplier. With the prevailing engine noise during a race, and with a helmet on, a buzzer would have been worthless. Downside of this setup is you would be have to mount an obtrusive light housing on the dash or steering column, however, as someone else mentioned, there are spots in the cluster where an extra warning light could be added.

Third - I'm not crazy about having the warning triggered only by low oil level, as there can be situations where low oil-pressure wouldn't be automatically accompanied by low oil level.
The solution would be to fit a suitable tee to the oil-filter pressure port - tricky but probably the best arrangement as I certainly wouldn't want an oil switch dangling from a makeshift splice in a plastic oil line or fastened at the cluster where it might dribble black goo on my pants or carpet someday.

Happy Motoring, Mark

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DrDKW