When the pressure switch clicks on, the pump was not running. I suspect you are saying that you are not sure the pump was running 250 msec after the switch clicked on.When it clicked on at 39 I am going to assume the pump was running I have no way of being positive as it’s down in the well outside, but the pressure in the tank goes up which I assume means it’s filling with water
You might be able to take a movie for hours with a cellphone. https://www.kiwigeeker.com/how-to/record-long-video-on-phone.html is one site I found that discusses this.
I don't think this following stuff applies to you, assuming the gray cable is going to the well. I can see there is no control box in line with the gray cable.
With a 3-wire pump, there is a control box with a start capacitor. That capacitor degrades with time. If that capacitor is getting weak, there could intermittently be a delay for the pump to not start. As it gets worse, the pump may not start at all. If you have a control box, it would be wired between the pressure switch and the pump.
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