Sounds like a blown fuse in the dash, no biggie, just take it in and it should be a quick fix
Wiring harness has come loose, blown bulbs, or bad wire.
Check the fuse for the headlights. It is probably open.
Fuse for parking lights probably blown.
Parking brake is on, Brake fluid is low, Hydraulic failure of the brake system.
Most likely a fuse or a bad ground.
Fuse, wiring, bulbs
Try applying parking brake
make sure your brake bulbs are in right way round. There is offset poles on a stop/tail bulb so they go in correctly but they can be forced in wrong way round activating the brake light side instead of the sidelight.
by design the DAY-TIME-RUNNING lights are not intended to be turned off by choice. When you start the 99 blazer with the parking brake on, the DTR lights are off. When you release the parking brake they come on. When you park again and apply the parking brake the DTR lights will stay on, unless you stop the engine and re-start the engine. Since the DTR lights are inter-wired to the regular headlights, they can not be defeated without affecting the regular headlights.
You can only turn off the headlights by applying the emergency brake. When the emergency brake is on, the headlights will not light. Otherwise the best of my expererience is that they are on all the time. If you have remote start, put the emergency brake on before you leave the vehicle and when you remote start it, the headlights will not be on, but the driving lights (if switch is on) will be on as well as the parking lights.
In this order only. Turn engine off. Depress parking brake. Turn engine on. Lights will turn off. To turn lights back on relase parking brake.
Check fuse # 3 , that is a 15 amp fuse for your parking lights if all 4 don't work
The head light switch is shorting out ,or a bad connection