There could be an internal short within the external connector socket.
If you can get a volt-ohmeter, test the continuity between the white with black stripe wire, and each other individual wire on the plug. You should see no indication of continuity, that is open circuit ... just testing the socket disconnected from the lamp failure sensor, no power applied, lights turned off. .... The VOM negative or black lead is touched or clipped to the W-B wire contact ... and then test each of the other wires with the positive VOM lead, one at a time, with the VOM set to measure resistance, .... say on the highest scale. ... VOM meters can usually be found at economical prices ..... a few dollars. ...
If your meter is analog...with a needle, it should swing full scale, all the way over. If the VOM is digital, it should read a high number when you test each wire.
If you do find continuity between the white with black stripe wire, and any of the other wires going into the plug socket, then you know something is wrong.... internally within the socket.
Also use the VOM in continuity mode to check that the white with black stripe wire is in fact making contact with the chassis ground. Do this first. maybe. If this wire were not properly connected to chassis ground, it might contribute to the basic problem. ... One test lead is placed on a clean, bare metal chassis ground ... maybe a screw or bolt, and the other lead on the white with black stripe metal socket contact.
The circuit diagram shows 5 wires going into the sensor: green, light green, yellow, yellow with green stripe, and the chassis ground wire, which is white with black stripe. ... The green and light green are the main current carrying wires. The others are part of the lamp signal activation circuit. ... The larger band looking metal piece on one end of the board is a current shunt .... which just passes the main tail light current load, and also produces a measurable voltage that is used to signal the status of the tail light current. .... and in effect, is used to control the on/off condition of the lamp warning light.
The circuit diagram is shown here. See p. 145.
It is not a complete diagram, but gives some idea as to the layout and function of the lamp failure sensor.:
http://www.camrymanuals.com/index.ph...=106&topicid=0
... see gen 3 section .... wiring schematic pdf.