I don't know if there's enough power available where you've tapped in, or not, but generally the rig should be grounded at its mounting bracket (to automobile sheet metal). If it's a temporary installation that may not be possible, but it should have a solid ground connection to the vehicle's frame somewhere, even if that is at the end of the power cord.
The antenna right behind the rear window might also be causing a problem. Can you try the same antenna (if it's a magnetic mount) in the center of the vehicle roof, instead? Less likelihood it will radiate back into the mike cable that way, as you'll be "shielded" from the antenna by the roof. It's also likely to work better up there.
A 21" whip on CB is really heavily loaded! That's only 0.05 wavelengths, kind of like using a 4" long whip on a 2 meter rig.