Thank you for your ideas from this discussion!
My problems started with buzzing behind the glove box and an intermittent DRL warning light that I silenced by turning my headlights off. Eventually the buzzing stopped and the DRL warning light was solid and the daytime running lights were inoperable.
I followed your suggestions and cleared the cold solder joints in the Daytime Running Light Module but still had the DRL light on my dash and no daytime running lights.
I traded out the DRL Relay located to the left of the glove box but the problem persisted.
I then checked the fuses located below steering column in the 01 Civic it is a 7.5 Amp fuse #12 and a 10 Amp fuse #3. Fuse #3 was the culprit and now the Daytime Running Lights are working perfectly with no DRL warnings.
It appears after reading many threads on this subject there are multiple points of possible failure in the circuit. Module (located to near the Hood release - Grey Box) - Fuses in cabin below steering column - and a relay located to the left side of the glove box (Grey Mitubishi Part RC-5102). It is less likely to be a problem in the headlight switch or parking brake but stranger things have happened.
I think the buzzing noise was intermittent power to the relay by the glove box but was only a symptom from the module power issues.
Thanks to all who contributed here!