Recently I noticed that low flow indicator on my city water gauge is moving
Ever so slightly. (It will sit motionless for 10 some minutes then move a tad or
Two). I've tried turning off the valves throughout my patio home, yet the only
One that seems to stop the movement is the valve that supplies fresh water to
The hot water heater. I kept this valve shut of for about 15 minutes to verify
That the dial had stopped & when I opened it back up I heard water gush into
The tank for a second or two.

I'm not sure what to make of this. Is it normal for a hot water heater to take in
Minute amounts fresh water, like it is topping itself off, an hour or so after
Hot water was actually used somewhere in a home?

Secondly, I cannot see any water leaking from the heater. So, if this is not
Normal I assume there must be a leaky pipe somewhere in the slab. What
Should my next step be?

To test heater shut the valve down on the heater and all faucets and see with its valve shut the meter stops this takes the hot water line question if the heater valve is good. If the meter still moves and the heater valve is good then there's a tiny leak somewhere.

signed 21 boat

If I helped to answer your question please rate my answer

If your hot water pipes are under the slab, then it is very possible you have an under the slab leak. Not fun.

Other possibilites are a defective Temperature and pressure relief valve and a remote possibilities are:

If the water company installed a back flow preventer somewhere or air in the lines. Unfortunately, the meter doesn't care if air or water is displaced or in what direction