I have assembled my own chase scenarios based on the code from the ones that come with the game. All have time of day running and are designed to be chasing for interesting driving not all out destruction but obviously you can play how you like. The Search and Detain scenarios are not meant to be quick. I designed them to (potentially) take some time. There is a chance that you will be able to engage the vehicle right away, if you go the right way.
Included are 31 chase-the-AI scenarios over Small Island USA, ECUSA, Utah, West Coast USA, Jungle Rock Island andbob.blunderton's LIDAR Tennessee map.
Small Island:
Hoppers
Vintage
Pigeons
Search and Detain 1
Jungle Rock;
Sports
Heavy
Rally
Search and Detain 2
East Coast USA:
JDM
Race
Trucks
Search and Detain 3
Utah:
Pickup Chase
Pigeon Chase 2
Sunburst Chase
Touring Chase
WCUSA: (Sometimes the AI drive really slowly on these)
Classic Chase
LeGran Chase
Muscle Chase
Track Chase
Race Chase Tennessee
https://www.youtube.com/watch?v=ROtM_tVlRHU
I have no idea why they show up in two different sections of the scenarios list in the menu of the game.
If you want more or chase racing is not for you then be sure to try out my time trial and drag packs. https://www.beamng.com/resources/highdefs-time-trial-pack.2772/ https://www.beamng.com/resources/highdefs-drag-racing-pack.3424/
If you would like to buy me a coffee or something this is my Patreon account, thanks very much. 
https://www.patreon.com/user?u=6000234