I'd go with the turn signal relay. It's one of the easier things to start with. It could just be sticking :-) It is located below the Instrument Panel, left of the Steering Column.
Removal Procedure
1. Remove the left closeout/insulator panel. A small 7mm bolt is holding it in place.
2. Disengage the turn signal flasher from the upper instrument panel carrier assembly.
3. Disconnect the electrical connector.
4. Remove the turn signal flasher.
Installation Procedure
1. Connect the electrical connector to the turn signal flasher.
2. Position the turn signal flasher into the slot in the instrument panel carrier assembly.
3. Slide the flasher upward in order to secure the retainer clip to the carrier assembly.
4. Install the left closeout/insulator panel.
the relay is available [http://www.partsgeek.com/catalog/1996/cadillac/eldorado/body_electrical/turn_signal_flasher.html|right here].
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