99 here too, and I dont think mine stayed on with the brights. I do have an early 99, and I know there are some other differences with late 99 models, so maybe this is one of them??? The fog light mod was one of the first things i did, so I dont remember if they were on with the brights.

"My family hauler can kick your family hauler's @SS!"
~~~~1999 Contour SE Sport~~~~
-KKM True Rev
-Custom cat back Flowmaster exhaust
-All Cat's fixed.
-SHO Shop Off-Road Y-pipe
-Many other Mod's done...