You also need a orange and white wiring harness to both lights under the headliner -behind the top bows on the drivers side and run down the drivers side windshield pillar to plug into the factory style rear wiring harness. All hardtops have this harness to match the factory interior lights that came on the car. I have some new originals of the orange and white wire.
I just checked I have a complete orange and white wiring harness from 61 (it looks like it to me) with mint original long rectangular chrome lights and the original lenses. They look like the ones for a 61 -in the picture above. They have two mounting holes and the mounting screws, sockets, original bulbs and lenses. They were removed from a car at least 30 years ago (by a friend of mine) and stored inside.
pictures of the orange and white wire on my 62 Impala 2 door hardtop (for your belair I am sure the wire is just a little shorter -but the routing is the same).
Paul