all other lights work. even the break light in rear window works.
no window brake light on a '55 olds, this is a 1985 cutlass supreme it could be you have a ground issue, a short, bad bulbs, or likely a blown fuse. If it's none of these take it to a competent friend or mechanic and tell them to wire the tail lights from the 3rd brake light. This could be the easiest way to fix it rather than replace the entire tail light wiring
I doubt seriously that your car is a 'Cutlass Supreme'. You might have a fuse that is blown, or both bulbs might be out.
1955? Cutlass Supreme not available back then. Did not come with a third brake light. Wiring has been altered and an investigation into the actual quality of 56 year old wires. Did you type in the wrong year? Wiring issues happen in nearly every kind of car. If the third brake light works and the lower ones do not work, the possibility exists that you have a malfunctioning turn signal switch. Yes the turns may well work but the brake light runs through this switch to get sub divided while turns are activated.