My guess is, the diaphragm in the pump has failed
16 years is a long time for a diaphragm to last. Have you noticed that pump occasional cycles for a couple of seconds for no reason (the pump breaker has to be on all the time for that to happen, btwt)? That's usually the first clue...'cuz as the system loses pressure from the failed diaphragm, it cuts on long enough to restore it. Diaphragm kits are available from WM etc, and only cost about $12. Just make sure you have the make/model/year of the pump handy when you order the kit, 'cuz they aren't "one size fits all," even among the same mfrs. However, allowing the water level in the tank to drop too low--below the top of the discharge outlet--will also cause the same problem...so I'd make sure that's not your problem before you do anything else.