The clue that moving your tool box makes a difference does provide a useful pointer. The feeder cable is not supposed to have any part in the radiating mode of the aerial, and in fact in many aerial designs, there are design elements employed to try to prevent it. Two things really, any emission from the non-antenna element can be additive or subtractive to the total RF emission, and usually cancellation, or at least partial cancellation occurs - maybe impacting in larger installations in notches in the polar pattern - strange directions where the signal is weaker, that kind of thing. The other thing is that matching the transmitter to the aerial is compromised. Are you matching the aerial, or the aerial and the feeder? In your case, both - as the location of the metallic lump in the boot (the tool box) impacts on the performance.
It suggests the ground plane is to a degree, uncoupled from the aerial. This always happens with mag-mounts, because they float over the top of the ground plane. One thing to check is if the DC resistance from the ground plane to the earth of the radio is a dead short. If it has even a few Ohms of resistance, then RF current is going to start to flow in the feeder cable, making it part of the aerial. It can happen easily on mag mounts on the boot - as rubber seals and greased bearings to make opening and shutting smooth do not ensure a good electrical contact. I've seen examples where the only metal to metal connection is the lock! If the mag mount is on the roof, then good grounding should be much more likely - after all, a metal roof is usually welded to the chassis/body, but you could have poor grounding at the radio end, so the earth /screen of the coax is floating - with the same result. I've used all manner of mag-mounts over the years from CB to ham to business radio, and the only times performance was poor was with grounding issues. Oddly, a direct ground is not actually needed. A handheld, working to a mag mount usually works perfectly fine, because the ground plane in this case is a virtual ground - a ground that functions as one, without any electrical contact. In practice, ground is insulated from electrical ground, and circulating currents don't exist in the feeder cable. Think about marine aerials and fibreglass hulls. From time to time, people use the sacrificial plate fitted to some boats designed to prevent the few metal parts in the water being eaten away by electrolysis, as a ground and often get very unpredicatble RF coverage as a result.
As for solutions for your problem. If the issue is the ground plane is poorly electrically connected to the radio ground, then extra bonding is worth a go - as soon as the tool box movement doesn't change things, you know you have stopped it - or alternatively, you can try a choke. A man sized version of those little lumps you often find in equipment mains cables - computers, power supplies - that kind of thing. If you can find an old, largish loudspeaker, you can make a simple and effective one. Dismantle the speaker back so you can get to the large donut shaped magnet. Be careful because the damn thing will magnetise your tools as quick as a flash. Pull out the ferrite ring, and then take the aerial feeder cable and wrap maybe ten turns of the feeder cable through it, then tape it up, nice and tight. Being magnetic, it will then stick to any bit of convenient metalwork. This works a bit like a shorted transformer, and reduces or often stops the stray RF travelling down the feeder cable screen. If you are desperate, and have an old speaker laying around - well worth giving this a try. These things are mega-magnetic, so will attract all kinds of debris and loose objects so beware.
For some reason I hate the term counterpoise - but it does describe what often happens. Aerial systems need balance and stability for repeatable performance. Almost every aerial type has some kind of balance requirement. The two legs of a half wave dipole, balance at the middle, and even a vertical on a ground plane has some point where balance is possible, if you could somehow detach the ground plane from what it's attached to (difficult of course). Picture your problem as a design with something loose attached to it - that balance is being messed with. You have to restore it.
A mag mount, in the centre of a vehicle roof, with the screen completely floating or 100% connected is stable. I suspect the reason body hole mounts rarely give problems is simply because the metal to metal contact just stops all this faffing around with random current in the feeder. The fact they're rarely central and have a very distorted polar pattern isn't as important to performance as we think!