if you have an exhaust pipe coming off the left side - check to see that the rubber between the exhaust pipe and the mounting bracket is not missing or worn.

 

My bike has exactly the same issue. The bracket was broken when I purchased my 1996 FLHR half a year ago. It was repaired by a welder but after two weeks it broke again. Left side. I noticed when the bike idles that the left side saddle bag is shaking pretty much whilst the right one doesn't. I have ordered a reinforced bracket (thicker) and installed it, so now that I see that the left saddle bag shakes a lot more, I hope that the reinfored bracket will hold. I bought the reinforced bracket at JP Cycles, part# 362-815. Your post was from 10 years ago, I wondered if you found a solution or maybe even the cause?

 

His last activity on the site was nearly 5 years ago. Good luck.

 

Thanks for noticing! I should check the dates first.

 

Mine was this.