Headlights always in DRL mode

Hi everyone!

I have a problem with the headlights on my '99 Camry. It has DRL and auto lights so it used to work like this, depending on the light switch on the steering wheel:
- OFF: all lights are off, headlights and dashboard
- Auto/DRL: dim headlights during the day, full lights at night, dashboard is lit. I have been using this setting for 7 years without touching anything
- ON: full headlights, dashboard is lit.

Here is what it is today, regardless of the ON/DRL/OFF switch position:
dim headlights as if in DRL mode always (day or night), dashboard is lit.

Basically, at night I don't have enough light (and for some reason I cannot turn it off).
Does anyone have an idea about what it might be?
Not so long ago I had replaced the brake light in the middle, not sure if this has something to do with such behavior...

Another interesting fact is that when I just turn the car on everything works normally. But about when I start driving it goes into "DRL mode", i.e. lights either turn on (if switch was in the OFF position) or lights dim (if it was in ON). I could not figure out the precise sequence of events like brake pedal or gear switch, but it looks like it may be something related.

Thanks in advance!
- C