Weird headlight problem, but DRL's do work

Ok, I've searched the forums and found a bunch of other people with DRL and headlight problems but none that quite matches mine. Here goes.
1. Daytime running lamps always work.
2. High/low beams usually work, except after driving for approximately 30 minutes at night with the headlights on, all of a sudden I hear a slight click (like a relay) and the lights switch to DRL only (parking lights are also still on). At that time the green DRL indicator lights up as well.
3. When this happens, after approximately 45 seconds the main headlights switch back on. They then usually work for any amount of time between 45 seconds and 2 minutes, then they click back off and return to DRL only. This continually happens until we reach our destination. Every time the headlights turn either on or off in this manner I hear a slight relay "click".
4. When I get in the truck, if I turn off the DRL's by depressing the emergency brake until the brake indicator on the instrument cluster lights, the high/low beams seem to work for a longer period of time before acting up.
I found one silver colored relay under the dash that causes the headlights to turn off when I remove it and I tried replacing it. This did not solve the problem. Is this scenario most likely a defective DRL module?

Thanks in advance.