If you do not get this information, then you have no way of contacting the person who sold or received the firearm. There is no problem with not being able to contact them, of course, unless you need their testimony to keep yourself out of jail on a bogus charge. Furthermore, without the other person's signature, you have no proof of an agreement. Without the agreement, you have no transfer of ownership. Without the signature, you have no proof there was an agreement to transfer ownership.
When you get the same information in your bound book that a Bill of Sale has, especially the other person's signature, then it will match it in court as proof of ownership, or proof of liquidation. It's just something you, yourself, wrote alone. As such, it is a record, not a legal document.