You are really only going to run into federal regulations for a manifest if you are hauling hazardous materials. When it comes to food you are generally going to cover this through the use of a bill of lading or an invoice for the shipment. It is just good business to have this paperwork in the truck anyway in the event that your driver gets stopped for a DOT inspection and the officer wants to see what is on board.
3.6 Traceability is pointing you in the direction of having positive control of your product during the entirety of the shipment. Is your load safe and secure, is your load making it from point A to point B? If you dont have a gps in your truck (which is great by the way) then the signature of the recipient of the shipment and confirmation that they have received their shipment in full will act as the traceability of the product from point A to B.
If you look down the steps of BRC 3.6 you can see that it is following the life cycle of the food product through your facility. Was it picked, was it loaded, did it get transported, where are the returns... 3.6 wants to make sure that you can trace everywhere that your product came from and everywhere that you sent it. Just make sure that you maintain the route summaries either electronically or in paper format so that you can fulfill this requierement. Documentation is key since they really will only believe you once you show them the proof that you maintain traceabilioty on prodct during shipment.