Jeff
I have a scheduled checkout of our HX zinc every three months. Half the time it doesn't need one, the other half it does. If you at least check it every three months, then you can begin to get a feel for what works for you. As far as I know, shorepower should NOT affect this HX zinc, since its only purpose in life is to avoid the corrosion from the seawater going through the HX. The other zincs on your prop and strut are the ones that usually go if there is an issue with shorepower (i.e., incorrectly wired shorepower, an incorrectly wired neighbor's boat or yours).
I have a scheduled checkout of our HX zinc every three months. Half the time it doesn't need one, the other half it does. If you at least check it every three months, then you can begin to get a feel for what works for you. As far as I know, shorepower should NOT affect this HX zinc, since its only purpose in life is to avoid the corrosion from the seawater going through the HX. The other zincs on your prop and strut are the ones that usually go if there is an issue with shorepower (i.e., incorrectly wired shorepower, an incorrectly wired neighbor's boat or yours).