The method I would use is as follows:
1. Strip the ends of each wire of 1/2" of insulation.
2. Twist the bare ends of the wires from the DRLs together (splice).
3. Slide heat shrink tubing over the wires 6" past the splice.
4. Slide the bare, twisted wires into a bare (i.e. not insulated) butt splice crimp connector.
5. Crimp that end of the connector.
6. Insert the supply wire into the other end of the butt splice connector.
7. Crimp that end of the connector.
8. Slide the heat shrink tubing back down the wires and over the connector.
9. Using a heat gun or other heat source, shrink the tubing over the connector.
10. If the connector is in a location prone to physical damage (i.e. rubbing against something sharp) protect the tubing with additional electrical tape or split hose.
Note - this method assumes you are using the correct AWG (gauge) of wire for the lights and the fuse; you are not using a suitcase connector to provide the supply (+12V) voltage; and you are using the correct fuse value.
Packages of crimp connectors and the crimping tool are available in all big box home stores, your local hardware store, and online.
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Good luck!