On 8/29/2005 7:01 AM US(ET), terri k via CarKB.com took fingers to keys,
and typed the following:

You will find many wires with connectors that aren't hooked to anything.
They are there for electrical options that you didn't get. More than
likely, the switch that operates the back up lights is not working. It
is usually near the base of the transmission shifter. When you shift
into reverse the shifter pushes a switch that turns on the lights.

As the other poster already mentioned, the shifter actuates a switch
that turns on the light.

The following will take a little trouble shooting skills and a
voltmeter:
To determine whether it is the switch or a connection to ground, put a
voltmeter on the connector to the bulb. When in reverse, you should see
12 Volts on connector.
In your case, you most likely will not see 12V because your lights are
not working.  If you do see 12V, there's something wrong with your bulb
socket.

With the car in reverse, measure from one connection on the connector
to a solid metallic part on the body (this is electrically connected to
ground). Try both connections to the reverse light.

On one connection, you should see 12V.
If if that voltage goes away when you take the car out of reverse, most
likely you have a bad ground connection to this bulb. The wire that
does not have 12V on it is your ground wire. You will need to trace
that wire. You'll find it will go to a screw attached to the body
somewhere. The connection may need cleaning or the wire might be
broken.

If you don't see 12V on any of the connections with the car in reverse,
the switch on the stick or the wire to it is broken.

Hope that helps.
Remco