You advise her that in Florida, failure to present her driver's license is a second-degree misdemeanor and an arrestable offense. You tell her that if she doesn't want to speak to you, that's fine but that's a separate issue. You also explain she doesn't have to agree with the ticket, that signing it is not an admission of guilt but one of receipt, and that she can always argue it in court.
You stress that there is no need for anyone to go to jail over running a red light in this instance and that is not your intention unless her actions dictate otherwise. In other words, you do everything possible to explain the situation to the driver so she can make a decision based on fact and not on someone else's opinion.
Finally, the driver rolls down her window and you engage in a friendly conversation. Even if she still wouldn't say anything at this point, you could explain the relevant case law, what your state Supreme Court has ruled, and include any other legal information to bolster your case for cooperation.
If it had gone badly because the driver continued to refuse to cooperate by not giving you her license then you would have followed agency policy and procedure on the matter.
Luckily for me, or for any member of our traffic unit, we have never had to escalate into a physical arrest (but we are always ready to make one). Trust me when I tell you, it's well worth the extra time and effort it takes to talk to the driver.