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I’m looking to replace a fuse on my logic board. I have a 13" MacBook Air: A1466 / EMC 2925 I can’t, for the life of me, find out which “820-xxxx” logic board I have. Please help!

Before you worry about the board ID which only helps you to find the correct schematic to trace out the fault which burnt the fuse to start with. Your system has a few fuses so knowing what your symptoms are can identify which fuse needs replacing. A common fuse is the displays backlight which you can see here (marked in Red):

Ryan Smith post some good images of your logic board (front and back)with your answer. That way we can see what you see. You also want to let us know which fuse you want to replace and why. Adding images to an existing question 820-3209 is for a EMC2559 (MacBook Air 13.3" 1.8GHz Core i5 (A1466) - Mid 2012) and may or may not use the same schematic. This is not an area where you want to guess. Your logic board is a 820-00165 and not a 820-3209 Update (12/10/2017) Here are some of the things to check