Is it legal to read a person’s arrest history and pull them over passed on that?

Question Details: I was driving with a broken tail light and got pulled over a quarter-half mile away from where the cop saw the tail light. When I got pulled over there were 3 police vehicles that pulled up next to me right away. I have had past drug history and was out on a bond. If multiple cops have seen the light and not pulled you over for it can a cop pull you over for it? How long can a cop follow you before pulling you over?

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