My 96 LS400 had the same problem for over a year. Of course I couldn't figure it out until I started checking this forum. It broke at exactly the same point, the accordian part of the tube. Other than the noise the worst part was at idle there was exhaust coming into the passenger compartment. I removed the tube, bent it over in a vise and reinstalled it. Car runs fine, I'll see what happens with the emissions inspection next year. Thanks for the incredibly helpful tips and diagnosis!
I forgot how quiet that car can be. :D