The bracket is 1-1/32" tall from the outside surface of the backing plate to the tops of the two radius bends. The material is 3/32" thick. The hole spacing is 2-1/8". The nut is 5/16" 24 centered in the hole and tac welded.
The Palmer book is just wrong about the air cleaner screw. I wouldn't put much faith in that book regarding K Models. The parts books can also have misinformation but for the most part are a reliable source. I've been fooling with K Models since 1974. Have restored a '53 KK, '54 KH and for the last couple years have been the new caretaker of an original 1956 KHK. If you haven't seen them they are all three in the gallery section of this website. The '53 and '54 are under Stan Diener and the '56 is under Roger Meinke. Roger was a previous owner but I am now the current caretaker of it. The point to all this is that it's tough to weed through the information and misinformation out there regarding K Models. You have to decide which source you are comfortable in believing. There are good books and there are bad books. Knowledgeable people and not so much. I have been involved in a fair amount of research on K's but never claim to know it all. I probably have forgotten more then I would care to admit.
Back to the 2402C screw. The parts book shows a slot head screw, the 1956 accessories catalog shows a slot head screw, my original '56 KHK has a slot head screw. A slot head screw is correct. If you think about it, what could be a better source of correct information then an original motorcycle to look at? With the exception of the pillion pad and a few pieces that got chromed (now replaced) it's a pretty darn good example of original.
Stan