Yes.
No.
"A creature is unaffected by this spell if it can't see, if it relies on senses other than sight, such as blindsight, or if it can perceive illusions as false, as with truesight."
Three very distinct conditions.
1) Can't See
or
2) Relies on something that is not sight
or
3) Has ways to percieve illusions
Only one needs to apply.
Blindfighting and Tremor Sense... Such old edition memories

.
About the "you have already been tricked"... And so? If i become blind, i still "see" more than one wizard? Do i see a wizard at all? I can't see, so i do qualify for immunity. "You have already been tricked" is no argument. The spell has not been cast on me. It simply creates 3 images and tricks one of my senses - sight - with continuosly shifting images. If i can't see the images, i'm no longer tricked.
WHAT? No! The images simply mimic the gestures of the caster, there are no 12 missiles appearing. The spell effects are not part of the caster. This yet again does not allow anyone to understand who is what, since shuffling prevents recognition instantly. Unless you happen to not be able to see or blindsight or truesight or any other condition that applies.
Mind you - i'm not saying that YOU should allow someone to close their eyes as a valid strategy. But it's undeniable that if you close your eyes you can't see, and that Mirror Images does not affect those that can't see. Everything else i've said it was always preceded by "i would rule" or "i would allow". Or closing with a "for me".
By the way: Bladesinger FTW (a pretty pathetic and sad attempt to go back to what this thread is about...)
Would you allow non-Elf or non Part-Elf Bladesingers in your campaign? Yes/No/Why?
Personally, i would allow them. Not that this has ever come into question on any table i played/dmed... Since the only person i've ever seen kicked out from a table was playing a bladesinger. And that person is known to all those i play with. And bladesinger have since aquired some sort of "laughable status" and nobody seems to want to play them (but not the person mind you - only bladesingers).