When you say you are responsible for designing the traffic signal steel structure, are you sure you mean that you are not responsible for laying out the arrangement for the traffic signal structure (height, length, signal head arrangement, plus designing the foundation?) It is not typical for consultants with the DOT to design the steel structure itself. This is usually left to the traffic signal structure manufacturer.... think someone like Ameron Pole. It is normally your responsibility to provide them with all the loading parameters related to your specific wind criteria. Also, don't reinvent the wheel, most DOT's will have standard details for different types of structures with varying lengths and signal head arrangement. 26ft is pretty tall. Is there a luminaire arm above the traffic signal arm? Also, 12ft is relatively short for the cantilever arm so I wouldn't think that galloping or vortex shedding would cause a lot of vibration. FL does have some pretty significant wind loads though.
Follow dauwerda's advice. You are going to need to pick up a copy of AASHTO for this. If your state DOT has approved the 1st edition LRFD, then you are going to want to look at chapter 10, 10.4.3 - Vibration for the discussion on this. Unfortunately, it may not answer your question entirely.