Coax cable

Correct. It should not be coiled up. However, I don't think you need to be so careful as to run it all over the cab. I let my coax collect together loosely. Some recommend a figure 8.

 

There's absolutely nothing wrong with wrapping your coaxial cable into a coil and zip tying it together. If anything it would help you eliminate common mode current. I do it all the time and my stuff works great.
Think of it like a garden hose. If you roll it into a coil the water still comes out the end at the same velocity.

 

You need a choke most of the time when you coil it, the problem is that it can act like a loading coil if there is no choke.

 

Go here and start reading from this point.

https://www.thetruckersreport.com/t...ads/static-on-cobra-29lx.340910/#post-5749237

follow the link I posted to understand what a choke is

 

' I need a beer and smoke not a choke !!!!

 

Most of the time the cable in the truck (oem) is junk. Its really cheap. I was told to have your cable in 4' increments and yes, Also to have about 20'. See, sometimes you can run i to the problem of the radio being to close to the antenna especially if your running 2 antennas. Thus solves that issue. Works for me anyways.