The first two or three of these may border on obvious, but I do have a couple of fresh data points for the last one.
"See, I told you so..."
No matter how unreliable the source or how tenuous the connection, any piece of evidence confirming any part of the theory is embraced.
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"Which is exactly what they'd say..."
Evidence contradicting the theory is taken as proof of a conspiracy to cover up the truth and is therefore also seen as confirmation.
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"You expect us to believe..."
Even if the evidence doesn't directly relate to the theory, it can still be considered confirmatory if it's odd enough or difficult to explain. Though not a conspiracy theory, we often see something similar with proponents of alien visitor theories. For example, some researchers argued that the interstellar object Oumuamua was some kind of alien craft not because it behaved like one but because it had properties that would be unusual for a comet or asteroid.
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"But the real history teaches us..."
Around 2000 (I remember because of where I was living at the time), while surfing I came across a Lyndon Larouche follower explaining history on a cable access channel. He explained that what he was about to reveal was not the history you get in classes or from books or from historians, but what really happened. I stopped to see what he had to say and my curiosity was more than satisfied when he started talking about troops Russia sent to help the Union in the Civil War.
I'd come across Lincoln's Cossacks before. They were a popular urban myth during the war -- the black helicopters of the day -- and somehow this obscure piece of 18th Century folklore had not only survived but had been reworked into a key piece of the popular modern mythology of Larouche.
I'd run across this something similar before. A few years earlier, I'd picked up a copy of a book called Proofs of a Conspiracy for a dime at a library sale. I'd always had a morbid curiosity about fringe groups and this was something of a two-fer, 20th century conspiracy theorists finding historical validation by reprinting a book of 18th century conspiracy theories.
This need for historical validation extends out to all sorts of groups on the fringe who want to be taken seriously. I'll try to dig into some examples in a future post.