A common problem with the Reatta headlights is the wires going into the connector for the headlight bulb can break. The movement of the headlights opening breaks the strands inside the wire cover (insulation). The outside looks fine but inside the wires are broken. This problem cannot be fixed by just taping the wire in place.

The wires breaking is usually caused by the wiring that plugs into the back of the headlight being routed wrong.

Correct headlight cable routing:
(See picture below)
The headlight cable should come up between the fender and the headlight casting and lay in the recess of the casting... then plug into the back of the lamp.

The wrong cable routing is:
The wire comes up behind the headlight and plugs into the bulb.

Repairing the broken wires:

When the cable flexes and breaks the copper strands it usually stresses both wires equally.

There are several solutions for repairing the broken wires. The simplest and cheapest is to go to a salvage yard and get a headlight connector from almost any GM car.  You need the connector, (probably drivers side), that has two wires going to both the high and low beam pin. Get it from a car with non-opening lights so the wires have never been stressed. When you remove it, get about 8-10 inches of wire with the connector so you have plenty to work with.

Cut off the old connector and splice the replacement in place. I like to solder the connection as it gives me more confidence that it will always be a good connection.

You could just replace the terminal that failed by removing it from the connector housing and splicing the replacement in place, but my concern is that when one wire fails, all the other in that connector have seen the same flexing and any of the other could fail at a later date.

My sketch below, for those not familiar with connectors is a cross section of a generic crimp. There are actually two crimps, the left crimp is on the insulation and acts as a strain relief so pulling on the wires does not disturb the wire crimp... which it the crimp to the right.