Most GM cars especially Pontiac's are prone to a clicking noise that sounds like a relay clicking on and off repetitiously at various speeds. This is cause by a faulty direction switch. It took Pontiac years to figure this one out. My first encounter of this was my friend rebuilt a steering column with used parts and his results gave him this problem. We had found the brass contacts were mushed down grounding out at times when ever the engine was running spiking the voltage in the wiring causing the relay to turn on and off all the time. The only remedy is to replace the directional switch with a genuine GM updated part. Then the clicking noise will be gone
Hello! First of all, congrats on owning a great car! That engine (3.8L Series II L67) is without a doubt one of the finest GM (Buick) has ever produced!
On to your problem - I think you have one of 2 things wrong:
1) a loose heat shield
2) a broken exhaust hanger
Both of these will cause intermittent (and highly annoying) rattling sounds, especially at low speeds or when the engine is under load (like going up a hill for instance). There are 2 hangers under the car located almost directly under the front floorboard. These are prone to breakage. There is also a heat shield in this same area - that is very prone to coming loose. If it's the heat shield - you can either remove it - or have it tack welded. If the hanger(s) are broken, you will need to take it to an exhaust shop (unless you know a welder :) ) and have those fixed - shouldn't cost you more than $20 either way.