A Noise, Vibration and Harshness expert is worth their weight in gold. Many people don't understand how hard that is. I have a set of chassis ears, and setting them up takes time. People still don't get the fact that time is money, and it should be easy... Vetronix actually makes/made a tool that analyzes the noise, or vibration, and can help pinpoint it.
I need to get one of those on the Schwinn Tempo. It has a rattle that sounds like it's up front, but the brake caliper doesn't rattle, headset is tight, bar, stems, brake levers, front hub, DT shifters all seem good.
I eventually noticed the BB is a little loose, but doesn't seem loose enough to make so much racket. I should look for ye olde BB hook spanner and cinch it down today (I hope it's not in storage in Vancouver, WA).
Of course I really need to set aside half a day, strip it down to a bare frame, repack all the bearings, lube all the threads, and put it back together.