Tail Light Issues
As mentioned above, the bulbs have to line up correctly in the socket, they can be put in wrong if you try.
Also check the grounds. There's one by the tail lights behind the carpet if I remember right. There's one beside the dome light and one behind each kick panel up front. I see these cause most of the problems.
A bad ground or the wrong bulb in the wrong housing can cause the flasher work as you're stating.
If you've got corrosion in the sockets solder in new pigtails sockets, you can pick up replacements at the popular autoparts stores


