Possibility a "circular" answer, but anything the routing protocol considers "external" to its inner workings probably is tagged external. By inner workings, I have in mind having knowledge of the topology and in conjunction some cost metric for that topology.
Something "external" often is information provided to a routing protocol that it couldn't calculate. Your example of redistribution meets this test.
Although you asked about EIGRP, OSPF is a more interesting example because it not only has different external types, but can even tag inter area routes different from "normal" intra area routes.
Thanks everyone but I actually figured out what I was missing shortly after I posted this question. I was looking at a couple of route table entries that were showing up as external eigrp routes even though they were in the same AS. I completely missed the "redistribute connected" on one of the routers which explained the external flag.
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