maysap

Hi, I have 94 corolla and the stop light is out on the left side. I bought the lamp but could not find out how to change it. I opened the trunck and loosened the carpet to see whether I can replace the light from behind. I see the electrical cable and the connector. I removed the connector but looks like the hole is too small for the bulb to come out. I tried turning the cable to see whether bulb comes out that way but no luck. Am I doing something wrong? I hope I donot have to open the light covers from outside to change the bulb as that would be bigger job. Would appreciate any help. I changed both the headlights few months back and that was pretty simple. So hoping to do the same with the burnt out Stop light. Thanks in advance