The 7 Pin Harness is used with larger rigs because they have braking systems. If your trailer doesn't have an electric brake system, the 7 pin plug is useless to you. However if what you want is to get rid of the hanging harness under the truck, just plug in the wires from the current 4 pin into the adapter you bought and get an 7 to 4 adapter from Harbor Freight.
That should get you the result you are looking for.
Else you would have to source a complete 7 wire harness and start at the front of the truck.
I key piece of advice though, Unless you intend to tow rigs that require a Brake Controller I would not install the 7 pin plug. it could lead someone to believe you have a brake controller and hook a larger rig that what your truck can handle. At the very extreme worst it could be life threatening if you tow a rig with brakes you cannot activate properly...
My 2 cents