The hydrant is leaking when water pressure is small. Is it normal?
That is the automatic drain valve, after use, automatically clean the body of water, to prevent winter cold. As you say, it should be the fire hydrant, and that will happen if you live in the north. In winter, the hydrant must be frozen.
To see which side leakage, if a drainage valve at the lower end of the drain, it should be with the pressure, but if the valve is fully closed die will not leak