Not positive but i would think that a power indicator light would stay on whenever the power switch was on. Would not think it cycled on and off with the thermostat.
As far as a problem, you'd know it with either scalding water/safety valve opening, or no hot water because something (thermostat, element) went bad. You're probably ok if water temperature is being correctly maintained.
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03 Itasca Sunova, Workhorse P32 with the 8.1 and 4L85-E
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