So, I was thinking about this more this morning. Is there a problem with my mount or maybe the cable that is causing this? I mean, why is the cable shield carrying RF in the first place? I already replaced the mount; should I replace the cable?
I get that a balun will probably be required to fix it, by why is it happening in the first place? Also, why would a dead short to the body/frame not fix it? Surely, that's a lower impedance path than the coax shield.
You have current flowing on the coax cable if the antenna has a poor ground plane. Being mounted on a box in the bed is not the best groundplane. That current is wasted energy.
Did you buy this antenna new? If not has someone removed some turns from the end of the whip to tune it?
RF current like any electrical current follows the path of least resistance/impedance. Because you have an insufficient ground plane for return current to follow the desired path into the shield of the coax, the current is following the outside of the coax and thus will have a lot of variability. Putting ferrite "baluns" will sop up that wasted current and turn it to heat. But that signal could be better put to use being radiated from the whip.
After you replaced the rusty mount did you check the resistance to the toolbox with an ohmmeter? Is the tool box bonded to the bed in more than two places? The more bonding the better. Check with an ohmeter. Is the bed grounded to the frame and the passenger box? Check with an ohmeter. You want zero ohms. You should be bonding with a large conductor 12 guage or better, the shorter the better.
Is the lid of the toolbox grounded? It could be floating at RF impedance even if it shows DC continuity. Install some metal finger stock (*) at the corners so that when closed it is grounded.
Just something to consider. If improving the ground changes the VSWR for the worse, it may indicate that the "Q" of the antenna has improved, the antenna is more resonant and bandwidth has narrowed and thus it may have to be re tuned.
If lower VSWR favors the lower channels, the antenna might be too long. If it favors the higher channels, it may indicate problems with the ground plane or the antenna is too short.
I am surprised no one has provided this link to the Fire Stick antenna tuning procedure. This should be read carefully and be sure to follow manufacturers recommendations.
Setting the SWR of Your Antenna© - Firestik® Antenna Company
Personally, I don't have the patience required to get these antennas to behave. I would be cutting a hole in the roof and installing a Larsen NMO27 by now. You still need to tune the Larsen, but the variability will be reduced.
(Flame suit on)
* Finger Stock is a product made specifically for RF grounding of cabinet doors.