I just recently went through a similar experience. It had been many years since I bought a gun through a dealer but this one I had gotten from GunBroker and needed the FFL transfer. Gun arrives and I go to do the transfer. Get to the part on the form where is says SS# (optional), ask the dealer about it and he says "If you've never had any problems with NICS before you probably won't need it". I haven't, so I left it blank.
I stood there as he called it in and they did ask for the SS#, I heard him say "did not provide". He was put on hold for a couple of minutes before he hung up and said "You've been delayed." What??????????? "Gotta wait 3 full business days and, since this is Thursday the clock starts tomorrow and the weekend does not count. So you can't pick it up until next Wednesday. If they don't call back and say 'Denied' then I can give it to you next Wednesday."
BTW, the FBI does not give the dealer a reason for the delay or denial so don't bother asking why. Nor is there a number to call where they will give it to you. There is an appeals process for denial, of course, at which point they do have to give you a reason.
The following Wednesday I picked up the gun. He had never heard back from the FBI, which is common, he said. I walked out reminding myself one more time why it is better to avoid involving the government in your affairs if at all possible.