When a cop pulls you over, the cop can search your “wingspan” – anything you can reach in the car. If the car is full of people, em can search pretty much the whole car. This is to protect the cop from weapons, etc. But if the cop finds something else . . .
As to the OP, I would likely search the car. More so depending on how many people were in the car; how long I had been following them; what they were doing when I was following them (i.e., ducking down beneath the seats, throwing stuff out the window); how long it took them to pull over once I flipped my lights on, etc.
A good example of profiling is a case where a cop saw a car break some law (forget which) and flicked on the cop car lights to have the car pull over. The car did not pull over for several miles (which translates, of course, to several minutes). During that time, the passengers in the vehicle kept looking through the rear window at the cop, then ducking down below the seat where he could not see them, then looking, ducking, looking, etc. When they finally stopped, he did search the car. Lo and behold, an illegal substance!
At trial, the defendants said, we were stopped because we were black. The cop said, no, because once you broke the law you acted funny, which raised my suspicions that you were hiding something in the car – that’s why you kept ducking down as you tucked it beneath the seat, and that’s why it took you so long to stop, because you wanted it safely stowed before I got there.
Court believed the cop.
The truth? Maybe a bit of both. You can be profiled for race, clothing, actions, etc. Depends on the circumstances.