Is the AC powered InstraHot unit powered off your battery bank or shore power?
Does it cycle on and off to maintain a hot water supply or does it only power up when it senses a demand for hot water at the facet?
The instahot is powered through the inverter. It remains active while the inverter is on. Once the water has reached temp it shuts off. When you draw water, more water is added and it heats on demand. The unit is insulated very well, and I was surprised that the water remained hot long after the inverter was shut off. But realize the unit is small, and is designed to provide on demand hot hot water. Most everything in the rig is 12v with the exception of the instahot, and the espresso maker, and thus we typically don't run it all the time. But in all honesty with 600 watts of solar and 2-250 amp hour batteries we have never come close to having to worry about power.
edit: The precision temp is a whole other animal. It is propane heated and the 'fire' is activated and controlled by the amount of water going though it. As the demand for water is present it fires up. With more water it heats even more. There is a point of course when one could push too much water through it and overcome the heating ability. But that is not an issue with a single shower.