This is eerily similar to an issue I am dealing with on the boat we just bought. It has a sporadic low OP alarm that just sort of randomly comes and goes. But, the OP gauge always registers normal. My initial thought was a wiring fault that was sometimes shorting out - depending on the vibration of the engine, wave action, etc. The way it comes and goes just "sounds like" a loose wire.
Going back a bit, just before we closed on this boat, the previous owner wired in a manual switch to turn on/off the fuel lifting pump. (Don't get me started on why he did this - that's a whole other story.) So, on our first few shakedowns with the new boat, I just got in the habit of manually turning on the lifting pump. We also started to notice this random alarm that seemed, by all indications, to be false. So, on our last couple of shakedown outings, I just turned the key off, which also turned the alarm off (and gauges). I preferred to turn the key on every so often, check the gauges, and turn it back off. This was better than listening to the alarm.
As we prepared the boat for the 4-day sail up to our home port, one of the things I did was correctly wire in the lifting pump so that it turned on when the key was on - per the schematics. Coincidentally, the alarm didn't sound after that. So, I chalked it up to some weird wiring issue that I either accidentally resolved, or that I would not be able to replicate. All gauges functioned normally and I manually checked the OP - all good.
About halfway up on our shuttle trip, the alarm came back. I lived with it for a while, but finally grew weary of it and just shut the key off. Blissful silence. But, after about 30 seconds, the engine sputtered and died. Of course, I had forgotten that I had wired the lifting pump in so it would not function with the key off. It took me an uncomfortable minute to recall this. But, I turned the key on, fired it up, and all was fine - except the occasional beeping.
This was such a source of stress that I finally just disconnected the OP wire from the alarm. Of course, this meant that the alarm would not sound even if the OP actually dropped. But, I was having to look at the gauge every few minutes anyway. This way, I didn't need to also listen to the alarm. And, the high-temp alarm would still work.
Anyway, all this to say that what I finally did was order a new alarm buzzer. Mine has two inputs terminals - one for solid tone (high temp) and one for pulsing tone (low OP). I had no reason to necessarily suspect the buzzer, but it was $30 to find out. Worst case, I have a spare buzzer. If that's not it, I will buy a new OP switch - another $30. I much prefer this approach to trying to track down gremlins. I will rule out these two pieces of hardware before spending a bunch of time looking for a wiring fault or doing any kind of in-depth troubleshooting. Yes, it's kind of throwing money at the problem instead of just doing a little basic legwork.
But, since I already ruled out ACTUAL low OP, I am not worried. Maybe I end up with a couple of spare parts and STILL have to crawl down there and chase an elusive short. But, I would rather pay a few bucks to create the chance of not needing to. I get enjoyment from a lot of boat maintenance tasks, but that isn't one of them.