not sure on the LS1 camaros but on my 95 T/A i had this same problem which was due to a bad wiring harness. the LT1 Firebirds used the 2057 twist in bulbs with the 2 prongs under them and the wiring harnesses were notorious for failure. i was told this by trans am creations in miami. they suggested i come down and buy an LS1 T/A style wiring harness and bulbs and that would fix it. sure enough that did fix it and it's been about 4 years and other than one of the used bulbs i got from them burning out, i havent had a single taillight problem since. it's possible your taillight harness has gone bad due to age or there is a bad connection. IIRC on the T/A the wiring harness is 1 piece but there is a left side plug and a right side plug so the lights are most likely in 2 separate circuits. i don't know if thats your problem or not but my taillights would do what you described as well as blinking in sequence instead of together. i would also randomly lose one whole side of lights when i applied the brakes.
*edit* i see your lights won't get brighter when you hit the brakes. mine would go out completely so maybe it's something else but it still could be the harness. are you sure the bulbs you have are dual stage?