Marathon should the lower element run all the time

I have a marathon question should the lower element run all the time, upper element cycles on and off but lower element never seems to stop, except when upper element cycles on. Maybe I should turn up top thermostat to above the lower one to see if the lower thermostat ever reaches temp and trips off. I am thinking the thermostat is bad and stuck on. Any help would be appreciated.

Has the T&P valve operated? Do you have a leak on the hot side water system? How are you determining the lower element continues to run? Do you have a voltage/clamp around volt meter? Are all the screw terminals tight and corrosion free? Dont electrocute yourself.

Has the high limit tripped on the top thermostat?

lets play 50 questions. LOL

If the lower element was always on, the safety relief T&P valve would be open since you'd eventually boil the water in the tank, and before that, you'd notice that it was VERY hot. On most electric WH, only one element is on at a time, but that doesn't mean you can't measure voltage, just like you can at a switch that is off.

Lets say they can be both on by design. I have 5000 watt elements in a little 30 gallon rig and keep them both on with their thermostats at 145 or so. heats the house.

If both elements operate at the same time, without rewiring the thermostats, it will draw about 40+ amps which will overload the common wiring for a water heater. If the lower element did not turn off, then the ECO would trip and shut the entire heater down. If you diagnosis is correct, the lower element is heating water, but it is going somewhere, the most common place is under the floor because of a a cracked hot water pipe. But if your lower element is burned out, it will ALWAYS have voltage to it, but it is NOT USING it. How are you testing it, with a voltmeter or a clamp around ammeter. You need both to test a water heater element.