Try what roadie said with the voltmeter, they are so cheap and help so much with troubleshooting so if you don't have one get one for yourself, you will use it more than you know.
I'm surprised that fuse 34 didnt fix it. Do you have the right bulbs for the rear stop lights? I found out myself that they are SRCK and not the normal pinout for the bulb and when I did a LED upgrade on my truck I blew fuse 34 from it shorting out with the led bulb. I like an idiot replaced the fuse 2 times before I decided to check the polarity and sure enough it was the SRCK as others said on here. Such a dumb design but thats car manufacturers for you. The fuse you were putting in could have been broken, I had fuses before that blew but had no visible shows of a break in the fuse and I wouldn't have known it truly was blown until I used my voltmeter on ohms to test resistance of the fuse and sure enough it never got a reading since it was a broken circuit with no continuity.
If those lights come on for the running light I wouldn't think the ground would be bad but it is still a possibility. Have you tried to get a known good bulb or a new one and put it in one of the lights and pull out the bulbs on the other light to troubleshoot it one light at a time?
That is how I would attack it, test the prongs in the light assembly for power and ground. Your pinout of the stop/running light in the rear is the same as this
http://www.vleds.com/media/catalog/...f42dca9de82fb58b1/3/1/3157ck_socket_9_1_1.jpg (note: you need to just turn the diagram to the side for your socket, the picture is sideways but it is still the same idea)
Another good thing to test is the resistance of the bulb, follow the same pinout in the diagram above to check out the bulb out of the socket for continuity between the low + and low ground leads as well as the same for the high side. It will be you testing resistance between each side so if you have the socket facing you straight you will test resistance of the top left pin with one lead of the multimeter and then the other lead goes to the top right pin. if you have no reading then you have a broken bulb.