I don't know how similar the circuit on a 67 convertible is to a 69 hardtop, but it's a strange one. On my 69 HT, power to the light comes from a connection to the rear harness in the vicinity of the drivers side rear wheel well. From there a wire goes to the door switches, which turn on the light by providing a path to ground. The two switches are NOT identical. One of them (at the end of the circuit) is a simple on/off that completes the path to ground when the door is opened, and breaks that connection when the door closes and the plunger is pushed in. This switch will have only one wire connected to it. The other switch has 2 wire connections, one comes 'from' the light socket, the other goes to the other switch. When the door is open/plunger out, it connects the input wire (from the socket) to ground and turns on the light. With door closed/plunger in, it connects to the other wire that goes to the other switch (so that when that door is open it also completes the circuit). If the wires aren't connected to the correct terminals on the "2-wire" side, or if the switches have been reversed (installed on the wrong doors) it can cause what you're seeing.