1969 coupe dome light

Sorry for the simple question. My 1969 coupe came without a dome light fixture. I put a bulb in the socket and it worked fine (though I was surprised at how hot that bulb got), so I ordered a fixture, which came as a chrome base, plastic lens, and two screws. In order to attach this, it looks as though you would just put the screws up through the lens, then through the chrome base, and then into two holes that are in the metal roof. The screws that it came with are too large for the holes, which tell me there is something wrong. My first thought was to just get smaller screws, but it would be hard to "find" these holes blind. It seems that just changing the bulb with this arrangement would be a pain because it would require removing the base and "finding" these holes by the feel of the screw tip. Am I missing a piece?