Wind Shake Effect Around Z Axis

I would like to create a "Wind Shake Effect Around Z Axis". I have a image of the leave in vertical position standing on its stem and would like it to have an appearance as if it trembles in the wind.
I applied Wiggle effect. However it wiggles/distorts in all possible directions but the Z axis. What would be my course of actions/direction to try to emulate a slight rapid shake around the Z axis in the front veiew.
In other words you look at the leave and see its right edge coming at you and left edge away of you and then in reverse. Pritty much like skewing in 3D with exception of X and Y axis.
I use AE CS6 on Windows.

Thank you for your reply.
Looks like I will need step by step direction as I was not able to successfully implement your suggestion.
Here is what I tried.
1. With the Wiggle Gelatin effect applied to my "Leaf" layer and 3D turned on I clicked "P" on the keyboard which opened Position in under layer's "Transform". Holding down "Alt" I pressed stop watch on the Position and entered your code:
    seedRandom(index, true)
    leafJitter=wiggle(3,30);
    leafJitterZ=leafJitter[2];
I got this error message:
     After Effects warning: Class'Array" has no property or methid named '2'
    Expression disabled.
    Error occured at line 3.
    Comp:'shake leave test'
    Layer:1 ('Green2')
    Property;'Position'
2. Same as all of the above, but I selected "Position" under "Effects" of the layer and got this error message:
     After Effects warning: expression result must be of demension 3, not 1
    Expression disabled.
    Error occured at line 0.
    Comp:'shake leave test'
    Layer:1 ('Green2')
    Property;'Position'
3. I deleted the Wiggle Effect all together and applied you three lines of code ot Position. This produced no results.
Please let me know where I messed up or you need more specific info on my set up?

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