I'm having the same issue on a 2005 SF GLS 2.7L. Though I just got the vehicle TODAY, I have a strong suspicion that there is a short.
My symptoms (the car was given to me for free today - so this is from the most recent owner): Brake light comes on. Battery light comes on. Intermittent chime of seat belt light / sounds. Sometimes the car doesn't start or dies suddenly. The first thing I noticed was the negative battery cable post clamp got super hot, really quickly. This indicates to me there is a grounding problem somewhere.
The very first thing I did just now was to unhook battery, remove battery tray (4 bolts, 10mm) and then remove the ground wire that goes from the negative battery cable to the fender well just under the battery tray. I ground the paint off of the area around the bolt with some coarse sandpaper, sanded the washer end of the negative battery cable that attaches to the fender, and the bolt threads that attach it all together, and then wiped it clean with acetone. Now apply dielectric grease to all the areas you sanded, and reassemble it all. This is vital to do on old / high mileage vehicles. Bad grounds can cause fires, blown fuses and relays and sensor / instrument failures.
Nevertheless the problem seems to persists (lights anyway, havent driven it anywhere yet to test it out if it dies). This is why I think it's a crankshaft position sensor - there is a visible "spark" - an arc between the nearest metal object and the closest exposed electrical component - the crankshaft pulley and most likely the crank sensor. I hope this helps you. I have yet to dig in further. Hope I will remember to update this post later when I figure it out.
