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Dave made some very good points but perhaps some clarification is needed for those new to the topic. What follows is a simplification of the RF theory involved. For more details see any textbook on antennas and transmission lines.
There is a phenomena known as the "skin effect" where at RF frequencies the current flow is present on the surface of a conductor and has a reduced magnitude deeper in the conductor. . The depth depends on several factors with frequency being one of them.
A coaxial cable used as a transmission line consist of an inner conductor and a shield. The transmission of power takes place between the center conductor and the inner surface of the shield because of the skin effect. . The outer surface of the shield acts as a "3rd wire" and if the far end is connected to a resistive dummy load does not have any current on it. Now when you connect the coaxial cable to an antenna like a dipole the leg connected to the shield is in effect connected to two conductors: the inner shield and the outer shield. The outer shield is now an element of the antenna and RF current can flow on it and radiation can occur.
Now what happens if you connect a hamstick to the center conductor and nothing is connected to the shield? Since the inner and the outer shield are connected at the cable end the outer shield will now be the other radiating element. There is an antenna called the "sleeve dipole" which is built using this technique.
The radiation on the shield is usually undesirable because it can lead to radiation in the shack and for receiving purposes it can lead to picking up noise because it is close to RFI generating devices around the home. The other drawback is that the feedpoint impedance of the antenna will change depending on the length of the coax and objects close to the coax cable. Any ground connection at the transmitter end or in the case of a VNA holding it in your hand will also effect results.
The solution to this is an RF choke. This is an inductor, placed inline close to the antenna feedpoint, which puts a high impedance in series to reduce the level of RF current. . The easiest implementation is multiple ferrite toroid cores with a permeability factor that is suitable for the frequency of operation. The coaxial cable passes through or is wrapped around the toroid. Only the outer surface of the shield is affected by this technique.
In summary to install the hamstick on a vehicle mount it in place with a good ground connection at the antenna feedpoint. Use an RF choke suitable for the frequency of operation. Run the coax to the operating position and then use your VNA to measure SWR. Set the marker to the desired operating frequency and then adjust the stinger for lowest SWR. If running you hand along the coax or holding the VNA significantly affect the results your RF choke is inadequate.