You have two very strong "rights" in conflict here. On the one hand, you enjoy second amendment rights to bear arms. On the other hand, your employer has a right to hire and fire whom he chooses.
Who would prevail has many answers. Is the vehicle parked on employer property? If so, then employer likely wins. If not, then you likely win. However, "win" is a funny word in the law. For criminal accusations a win is getting to go home from the courtroom, but in civil law a win is money damages. That means if you are fired for the wrong reason, you are still fired. You wold have to commence a lawsuit to get money damages for being wronged, and that is not an easy thing to do.
Even rights enumerated in the united states constitution are subject to reasonable regulation. Employer rules limiting weapon possession in relation to your employment are upheld when deemed reasonable, a very slippery word in the best of circumstances. Because Florida has weak worker protections, you just might be out of luck and have to go undefended during your daily commute if you wish to keep the job that causes the commute. Oh, the irony!
The above is provided for educational purposes only and is not legal advice nor makes you a client of the Mosca Law Firm, PA. Please consult with a lawyer in order to obtain confidential legal advice that is tailored to your specific situation and facts.