A 2004 Chevy aveo with around 78,000 miles has the following issues:
The Daytime Running Light indicator (as well as the lights themselves) randomly turn on and off. This is a slow thing and has never happened rapidly. It usually happens after five to ten minutes. This doesn't affect using the lights as normal if they are manually enabled.
When the gas light should turn on, instead the check engine light turns on. No gas light ever comes on.
Occasionally when the car is started the HVAC fan doesn't work and won't start at all. Turning the fan level from 3 to 4 (it's highest setting) creates an audible click that seems to be coming from behind the steering wheel. This happens while the fan is working, but I decided to include it for completeness.
I've included all of the symptoms here because this seems to me like they might be from a shared electrical issue, however, my experience is mostly in computer repair.
Is it possible for these symptoms to stem from the same issue? If so, which system should I investigate first and what should I look for?