LIKE TO SEE WIRING DIAGRAM FOR 1996 RS1300. FROM BATTERY TO HEADLIGHT

Have you checked the relay in the circuit. You really need a schematic of the wiring diagram. Electrical can be tricky without the wiring diagram.

Honestly, there simply not much difficulty to the way headlights are wired on any vehicle. Standard headlights receive positive 12v from the headlight switch directly (or through a relay, if you have automatic headlights), and the switch receives power through the fuse block from the battery. When you turn the headlight switch on, you should get 12v at the input connector to your headlights. If the headlight connector is not receiving +12v at the connector when you turn the headlight switch on, check the fuse, the switch, and the relay. If the headlight assembly is receiving +12v at the connector, check the bulb. If the bulb tests good with an ohmmeter, check for a broken ground wire. That is simply all there is.

I'm going to post this in the clarification section. I don't have a wiring diagram for a 96 Grand Cherokee headlight circuit.
The 95 models used a circuit breaker built-into the headlight switch. The 97 models used a fuse in the fuse box. If your model uses the headlight circuit breaker, a short in one of the headlights or the wiring harness would trip the circuit breaker in the switch. You could unplug one headlight at a time to see if it continues to go on and off.

Try this link http://bbbind.com/free_tsb.html

http://www.autozone.com/autozone/repairinfo/repairguide/repairGuideContent.jsp;jsessionid=452E33882A1EC92BA14E1C83E482A245.diyprod5-b2c15?chapterTitle=Wiring+Diagrams&partName=Chassis+Electrical&pageId=0900c1528003a3a9&partId=0900c1528003a2df

Is this the headlight bulb replacement or headlight (assembly) replacement? For bulb replacement:
1. Disconnect negative side of battery.
2. Open hood.
3. Reach behind the neadlight assembly and disconnect the wiring connectors.
4. There is a locking ring around the back of the headlight assembly. Turn this counterclockwise.
5. Gently pull out the bulb.
6. Insert new bulb into the locking ring.
7. Place these back onto back opening and turn clockwise making sure it is flush and totally engaged.
8. Replug wiring connector.
9. Reconnect negative side of battery.
10. LIGHTS!!

I would take a look at your headlight dimmer switch. The dimmer switch works independent of the DRL system.
Below is the wiring diagram for you vehicle.
Good luck and let me know.
Regards,

Here's a link to a pdf file containing the headlight wiring diagram for your year model Dodge Ram 1500..
I can't help but notice that you say you've replaced the headlight relay? That's quite odd, because there is NO headlight relay on this vehicle- only a 40 amp fuse located in the power distribution box that sits behind the battery inside the engine bay.
The switch is notorious for burning out because there is NO RELAY on this vehicle, and there is a recall (#819) but this only affects 3500 models even though the headlight wiring is the same for 1500,2500 and 3500 model Rams.
Here are two more links that will help you troubleshoot your headlights problems.
HereInformation on Putting a Relay in the Wiring System