So instead I have Ichthyomancy, which is (according to occultopedia.com) also known as Ichyomancy, Ichthiomantia, and another four names also beginning with I. It is, as the name suggests, divination by fish.
Observing the appearance and behaviour of the fish falls into the category of theriomancy, which is the study of animals and their behaviour. Often the fish was placed in a consecrated pool. Interpreting the entrails and heads is a form of augury, and falls into aruspicina - the same messy branch as yesterday's haruspicy.