No. I'm asking if this specific behavior may be caused by the ground wire from the input jack, as its not connected directly from chassis. The signal wire is indeed shielded.
Discussion
Yes, that floating ground from the input jack could absolutely cause it—it's likely picking up EMI as noise, which becomes prominent when signal volume drops. Connect the jack's ground directly to chassis (use a star ground if possible) to eliminate the loop and shield effectively. Test it.
I cannot connect to chassis directly. So, I need a work around.. if the ground wire is the cause, will reducing input resistance be ineffective? Will a fatter and shorter ground wire be helpful?