'96 Eldorado--disarming running lights
Under the hood there is a fuse and relay box. Inside the lid of the box is a diagram of the relays, and one is labeled DRL for Daytime Running Lights. Sometimes GM labels this a type of headlight relay.
When the DRL's are on, the relay in question connects the high beam filaments together in series, delivering 6 volts per bulb. When you turn the headlights on, the DRL relay is shut off.
If you simply remove this relay you will have no high beams. All bad.
Now VERIFY which relay is the DRL. Crank the car and release the emergency brake - which will inhibit the DRL's (on a Caddy you probably rarely use the emergency brakes anyway). With the DRL's on, pull the relay, make sure the headlights go out.
If your Caddy will do that, the fix is simple.
Look at the relay. Figure out which terminals are for the COIL. Post a reply here if you are not sure.
Take a pair of side cutters and clip off either one of the two COIL connections to the relay. Put the relay back in. Now the headlights work normally but not the DRL's.