My problem is mainly that while approaching the patrol car, some of the flashing lights disappear.

 

Here is a video: 

 

 

The white corona is not realistically supposed to show through the vehicle, which is why it disappears when you approach the vehicle to a certain distance. For other lights, it seems they also go into an "orb", which is also part of the rendering issue. Here are some things you can try to fix it with, or atleast some I have done.

 

1. Find ELS.ini (if the vehicle is ELS) and find LodCoronaInitDistance and increase it from whatever value it may be. I believe it is default as 10.
2. Change your render distance in your "advanced graphic settings tab" of the settings menu within GTA. Increase it if you can if it is relatively low.
3. Increase LOD distances overall, though it doesn't necessarily look as if the lightbar itself disappears.
   1. Go to \mods\update\update.rpf\common\data\levels\gta5
   2. Find and edit vehicles.meta
   3. Search for the model name of the car (Ex fbi2)
   4. Change the values of <lodDistances content="float_array"> for that model. Depending on the computer, you may only be able to handle certain distances. (See spoiler) 

Spoiler

<lodDistances content="float_array">

        500.000000         

        500.000000         

        500.000000    
        500.000000    
        500.000000
        500.000000
      </lodDistances>