Are there any books that go into this topic in depth, typically I have
seen 1 or 2 paragraphs devoted to the topic.  Maybe a source with a
conceptual focus.


For instance some questions: Does the Effect Modifier have to be
dichotomous or can it be continous?

I think it can be continuous because of the following scenario:
Say you are testing that Coffee lowers body weight only in people with
low kcal intake.  Therefore you have to test for interaction because
Var_kcal's beta alone would not tell you if calories affects coffee's
effect on Bodyweight - it would only tell you of Calories' effect on
bodyweight.  In this case you would have both product terms being
continuous, so it is possible.
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