The guy who signs your paperwork must be 2nd or 3rd degree registered with the IBJJF. I believe the 2nd vs 3rd thing comes down to whether or not you were registered at brown belt. If you were registered as a brown belt, a 2nd degree can sign. If you are coming in fresh at black, you are considered provisional and it takes a 3rd degree to get your card.
Whoever signs your paperwork does not have to be the same person who promoted you directly. I think technically it is supposed to be the same person, but in practice a lot of people get someone else to sign if their immediate instructor is not registered with IBJJF at the appropriate level.
I'd ask your instructor and see what his situation his. If he is not able to do it, perhaps his instructor could?
It's optional and a bit of a hassle so a lot of people just don't bother. But from experience now I have run into zero cases where someone registered and told me five years later he wishes he had that $30 back. What I have run into at least a half dozen times by now is someone who did not register upon promotion and five years later really regrets not doing so because he can't sign for his students properly in the IBJJF.