bright light becoming near and more intense in rear veiw window of car

This is an experience that my husband nor I have forgotten and I have felt compeled to share.  My husband and I were driving back to Arkansas from visiting relatives in Shreveport, La when this occurred.  We were in a Mustang fastback, which is relevant to this story as we had a large window from which to veiw what transpired. About 10 miles out of Homer, La., we noticed a large, bright light in the back window of the car.  At first we assumed it was an aircraft that was flying low.  The light grew larger and larger which really got our attention but instead of staying on an apparent flight plan it seemed to be following us.  The roads in the area are extremely curved and the light stayed right behind us.  After what seemed forever, and the light had definitely brightened and was coming closer and closer  it just  zipped off into the Western sky.  We will never know what it was. What we do know is that it stayed centered in our back window no matter which way we turned or how fast we drove.  A very eerie feeling!
Date is approximate.  PD