Zero experience with banners on bikes or trailers behind bikes. But the principles learned in automobile racing are relevant. There are illustrations in my book Designing and Constructing Special Cars, BT Batsford, London and Robert Bentley, Boston; see if your library has a copy.
***
I'm going to treat this as a banner on the bike itself. A banner on a trailer might be more advantageous still, or more troublesome, depending on particular cases, as will soon become clear.
Calculate where the centre of gravity, CoG, of your bike is, horizontally and vertically, including your own weight.
Calculate where the centre of (aerodynamic) pressure, CoP, falls, horizontally and vertically, including the surface area of the tubing, the banner, the tires, the rider, and all normal luggage. You may treat the bike with the banner and you and the luggage and the bike as a plane (flat surface).
Now you have two points. In real life they wander around a bit depending on speed, road surface, and wind vector. For the sake of a first approximation, we'll assume that the static calculations you've made above represent an average of real-life points.
The first thing you want to establish is that the CoG and and CoP do not coincide. This is an unstable condition, resulting in positive feedback, where each unwanted action and reaction magnifies the error.
Furthermore, the CoP MUST BE BEHIND THE CoG, or any gust of wind, even a small one, will unseat you. This is the reason rear panniers from competent purveyors of bike gear are large and front panniers are lowriders, small so as to catch little wind, and low so that their weight don't cause dangerous steering conditions.
The vertical height of either point determines a lever arm perpendicular from the ground. Make an experiment; hold the bike up with one hand but lightly, and with the other hand press against the saddle and then against the bottom bracket. See how easy it is to push the bike over if the lever arm is long, and how much more difficult if the lever arm is short.
A CoP a little way behind the CoG makes the bike stable through generally negative feedback.
There is also a horizontal lever arm between the CoG and the CoP and, given that the CoP is properly behind the CoG, the longer the lever arm is the more sluggish the bike's reaction to the controls will become until it becomes a beast you don't want to ride even in a parade on city streets.
