I am having a problem out of my 1966 Chevy Impala I dont have brake lights, signal lights and the reverse lights flash on and turn off. Hazards work when pull the hazard switch on and the corresponding blinkers signal in the direction when I turn it on.Help
Welcome to the site. You're also now a member of the "my damn impala brake/signal lights aren't working" club. Lots of those members in here too.
There's quite literally 6-12 spots that can, and have, failed for a lot of Impala owners. You're not alone, that's for sure.
While I could walk you through the schematic and some testing the fact that you actually have that Hazard Light option is tricky for me. I'm not sure where/how that is wired in.
Naturally, the brake light voltage and the turn-signal light voltage is the same. The 'tail-lamps' aren't as bright of course and have different testing. You didn't mention those so I'm suspecting those are A-OK. (?)
Its common for the brake pedal switch to get dirty and not let the power feed up into the column. Also VERY common for the 50 yr old plastic turn-signal mechanism to get cracked or melted. (that mechanism just under the steering wheel)
It's also common that there is corrosion at the brake light's contact with the tail-light housing there in the trunk.
Do you have a 12V test light or multi-meter? You're most likely going to need one.