Question
You recently answered a similar question.  But my situation is different.  My pump is at least 10 years old.  Never had a problem before but now it is cycling off after about 10 seconds.  Then maybe 5 minutes later, it goes on again (for 10 more seconds) & so on & so on.  No switch that I know of.  Any advice?

Answer
Interesting situation.
If the pump cycles on and off, on it's own, you do have a pressure switch. Now, if it is doing it only while the sprinkler system is on that's a different situation.
An easy way to tell if your system is pressurized (operated by a pressure switch) is to look for a water tank. It would normally be located by the pump and is made of steel. The pressure switch is located on the same plumbing as the tank with wires in and out of it.
If you could check for the tank and let me know, it would help me resolve the problem. There are so many scenarios depending on what system you have. I don't want to have you checking things that may not be applicable.

Matt