1998 Toyota Corolla Electrical problem

Electrical problem
1998 Toyota Corolla 110000 miles

When I turn my car on the daytime running lights come on and then about 10 seconds later (when the dashboard lights come on) the headlights go out. All fuses are fine. I think this may be a relay issue or a wiring issue. All other lights work. I have (so far) only checked this at night but I think it isn't a problem during the day. I *think* during the day everything may be working fine.

Does anyone have any advice about how to at least diagnose the problem more and see if I need to replace a relay or just have the wiring checked. How can I check the relay (if that's what the problem even is?)
Thanks,
Mark