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I use it, but I have to admit I'm not much of a fan. All it has done is annoy me by forcing me to stop my flow and look-up a secondary field.

I think there should be a 3rd option of just having a second password. Better yet, add a few other options as well.

What additional security would be derived from a second password?

A second password is just another form of a second factor (in 2-factor authorization)

2 factor auth is "something I know" (password) and "something I have" (token/device to provide a one time password)

Two passwords you know is not 2 factor auth

No, it's one factor, twice.

Not even twice, just split in two fields :)