Singer model 12 or 12K and originally called "New Family" uses a Singer 12x1 needle. I've found the most commonly available new old stock needles are "Boye" brand with number "20-1/2" on top of lid. The red 20-1/2 contains 3 or sometimes four needles sizes 12, 14, & 16. The black 20-1/2 contains sizes 14, 16, & 18. 4 needle tubes contain 2 of the middle size. These needles are currently not manufactured but hopefully someday the 12x1 needle will rise again.
Jon