A possible different version of the Gish Gallop Fallacy?

Yes, but the links seem to give the claims more credibility than it otherwise would have. After all, if they say the document is in there somewhere then maybe its true? I just don't have enough time to find the needle in the haystack, but I am sure this someone has. So one whom might be biased to want to believe the claims can appeal to faith that the document is in there somewhere? Or they can just repeat the claim that the document is in there somewhere based on trust, faith or a desire or assumption for it to be true? 

This is similar to the "Google it" (implied or stated) response

CLAIM: Evidence of lizard people is overwhelming. There are thousands of websites and youtube videos providing evidence.

Once my coworker tried to "introduce me to Jesus" by providing me with overwhelming evidence that God existed. He provided me with printed out listing of over 500 books on the topic, claiming every one of these books contain "compelling evidence." Of course, without investigating each claim, the only reasonable position is that we have no idea if any of this is legitimate evidence for the claim, so it should not sway us, but it clearly does sway people—which is your point. This seems to be more of a cognitive bias, but can be used in argumentation:

X is true
Here are an overwhelming number of resources that claim to provide evidence that X is true.
Therefore, X must be true.

This is fallacious, and perhaps a general non sequitur .

This can be a valid heuristic if we change the conclusion to "I will accept X as provisionally true based on the reliability of the sources referenced." The biases come into play when evaluating the sources.

Back to your original question: Is this a unique fallacy? I don't know of any but perhaps this does deserve it's own name. It does seem to meet the criteria.

Sweet! Can I name it? lol

Go for it

I've heard this being referred to as the Snow Job, and you actually list it as a B-list fallacy in your book.

Thanks! I tend to ignore the B-List:

Snow Job: There are several uses of this phrase: 1) “Proving” a claim by overwhelming an audience with mountains of irrelevant facts, numbers, documents, graphs and statistics that they cannot be expected to understand. 2) A strong effort to make someone believe something by saying things that are not true or sincere. Or 3) an attempt to deceive or persuade by using flattery or exaggeration. All of these uses are closer to lying than a fallacy.

The "fallacy" would be "because there are so many documents then it must be true" - I remember questioning how many people actually think. The other option is "because there are so many documents then it must have some truth to it." This MIGHT be a decent heuristic , depending on the sources. For example, "virtually every scientific journal confirms that there is no evidence for the claim that vaccines cause autism - here are links to 100s of articles." That would not be unreasonable to accept this at least provisionally (assuming the links are legit).

How about the "Haystack Fallacy"

See my comment above. Rationalissmo was correct - there is already a name for this: "snow job"