Probably because he ran her plates and got a driving record and warrant check. That's why it takes so long between the first time a cop comes to your window and giving you the ticket.
As for why he didn't say so right away the second time, probably because she was making faces or otherwise indicating that she was mad. And that is when he starts asking more questions.
I bet the minute she refused to put out her cig, he was going to give her a real ticket.
So, she's making faces and is angry, and that's your greenlight/"difference maker" for the cop to give her a ticket? Wow. This is exactly the "playing nice" game that I've described in a cousin thread.
If the cigarette is such an issue, why didn't he ask her that before she rebuked his grounds for the ticket? He's power tripping the whole time after she hints that she's not pleased, and you're greenlighting his power trip because she wasn't a bootlicker.
This is victim blaming at its finest... she's rightfully angry, and you're saying we can't blame the cop for not keeping his cool?