I appreciate the responses. I checked the ground wire from my neg terminal to the radiator cowl. It was loose. After fixing the loose connection the problem with the reverse lights flashing with the tailights disappeared. One thing I did notice, the left tailight did not blink as "bright" as the right side. Any ideas?
Also, I noticed that I do not have any reverse lights. The car has been in storage a long time, so I'm not sure if they just stopped working or have been out for a while. I wish I knew more about electrical stuff. Any help on both issues would be appreciated.