Both past tense and historical present are talking about things that happened in the past. Yet I've been told before it's incorrect to use them together.
Is it incorrect to use them either in the same sentence, or in close proximity to each other within a paragraph?
An example of this might be:
He walked into the bar and found a stool to sit at next to me. He looks at me and then punches me in the gut.
or
He walked into the bar and punches me in the gut.
In informal contexts, it's perfectly fine to start telling a story in the past tense, and switch to historical present shortly after you start it. I really wouldn't recommend switching between the two randomly.
I'd say your first example is grammatical, even though it sounds slightly awkward—the switch isn't positioned at that good a point (this is probably why it was recommended you ask this question at Writers.SE—exactly where and how to switch is more of a style question).
I don't think a native speaker of English is at all likely to produce your second example. It's ungrammatical because you're connecting the two different tenses with a conjunction, and it doesn't work to connect a past and a present tense together like that, without repeating the subject.
But it's possible to use them in the same sentence; for example, the following seems fine to me:
The other day, I was sitting in my favorite bar drinking beer when this guy I know walks in. He finds a stool next to me, looks at me, and then punches me in the gut.
