Select a spotlight fixture designed for installation under eaves. This variety features a swiveling base that will allow you to point your light. Remove the screw-in trim ring from the front of the fixture by twisting it counterclockwise.
Turn your paint can upside-down and trace around the outside of the threads on the back of the trim ring, from the light fixture in the center of the bottom of the can. Use a hole saw, the same size as the traced circle ,to drill a hole through the metal bottom of the can.
Fit the cut can onto the face of your fixture, with the bottom toward the socket. Twist the trim ring back into its threads -- inside the bottom of the can -- to hold it in place. Screw a spotlight bulb into the socket.
Zip tie a 4-inch C-clamp to the back of a round junction box, using two zip ties through the holes in the bottom of the junction box. Wrap the ties around the back of the C-clamp, on the side opposite the screw clamp.
Feed the wire end of your replacement cord through one of the punched out holes in the side of the junction box. Match the wires from the replacement power cord to the leads from the back of the spotlight fixture. Use a wire nut on each pair -- white to white -- black to black -- and green to green.
Tuck the wires into the junction box, and fit the base plate of the light fixture over the open face of the junction. Install the two mounting screws through the base plate into the junction box. Tighten them with a screwdriver.
Fit the C-clamp onto the pipe of your lighting bridge. Tighten the clamp, to hold the light in place. Plug the power cord into a socket on a dimmer pack, and turn the light on. Focus the par can by turning the open end of the paint can.