smk17 wrote:
Few weeks ago I had to replace the pressure switch on our water pump
because it would run around 120PSI non-stop.

So I installed the new pressure switch (40/60). I set it to turn on at
40PSI and shut off at 60PSI.

Now, when someone is on the shower, washing machine filling up, toilet
flushed, etc, the pump runs for 5 seconds till it reaches 60PSI, then
it shuts off. Pressure quickly falls to below 40PSI and it comes back
on for another 5 seconds, shuts off at 60PSI. Quickly goes down to
below 40PSI and turns back on. Repeating this over and over and over.

I know I have set it to do this, so it may seem crazy to ask if this
is the proper way this should work? It actually seems to be working
perfectly, on at 40, off at 60. But the constant on/off/on/off/on/off/
on/off/on for several minutes straight just doesn't feel right to me.

Is it running right or do I have some sort of problem with the holding
tank?

Thanks
Hmmm
Your problem is more likely bladder tank, not the switch.
Think logic.(IBM motto)