I have an 06 FLHT, the factory radio is made by Radio Sound and there is a 40w x 2 amp mounted under the tour pack. The front and rear speakers are hooked up in sequence and the rear pods have a separate volume control.

When I turn the bike on (radio off) I get static from the rear pods. Occasionally with the radio on I get little or no volume at the rears. Where to begin? I checked the connectors at the front speakers and everything is clean and tight.
ETA: this happens even with the engine off. This is a non-EFI model if that matters...

 

The 06 has an HK radio? Radio sound was from 1988 to 2005. Not saying you don't have one. But it's not OE. Have you had the fairing off yet to verify it's a radio sound? In regard to your issue I'd start with verifying which one you have in there.

 

It is indeed Radio Sound

 

Hmmm that's a first. I've installed several systems on an 06 Ultra and they were all HK. Sold most of the radios right here on the forum. Anyway back on topic. Your issue is static from the radio and intermittent volume in the rear speakers. With audio everything is consistent until it's not. Meaning there are some connections that have became loose in the system somewhere. Possibly in the radio itself. Who knows? It's a process of elimination. I'd check all my ground wires and connections to the radio and the speakers first. If they are in good shape I'd start looking at replacing the radio or getting it fixed.