I would think that rather than limiting deflection, you'd be concerned with vibration- make it too flexible and it's going to be flapping in the wind. Is that covered by the signpost standard(s)?
We use L/240 for soundwall posts at our DOT. I have seen similar discussions here indicating these sorts of cantilevered posts get no more than L/180 to L/150. How far do you want to go?
NCHRP Report 412 suggests that total deflection at the free end of single arm sign supports and all traffic signal arms be limited to 8" (200mm) vertically, when the equivalent static design wind effect from galloping and truck induced gusts are applied to the structure. They offer no recommendation for a displacement limitation in the horizontal direction.
I cannot find a deflection criteria for signs in AASHTO's Standard Specifications for Structural Supports for Highway Signs, Luminaries, and Traffic Signals. There is a deflection criteria for luminaires under wind load, but not for signs. However, there is extensive treatment of wind induced vibration and fatigue.
NCHRP Report 412 is what this section of AASHTO is based upon.
What was mentioned in my previous post is all that is available in the entire AASHTO code regarding deflection requirements for highway sign, traffic signal and luminaire supports. Thought you might like to save a buck, in case you changed your mind about purchasing this code.