It seems to me that something which handles light is the way to do this. You want to mimic light as it plays across a surface, and a 3d package is probably best suited to this. If you want to mimic this by hand, you need to understand what light does to an object, and the quickest way to get a feel for this is to freeze-frame videos of the effect (youtube etc).
An animated gif can be created by creating individual image files (frames) and then using a tool to composite them. I have in the past actually used visual basic to programmatically composite images and animation to output frames and then a 3rd tool to composite the set into an animated gif. The hard part is simulating the light.
Exactly how you do this depends greatly on the software you have available to do this, but were I to attempt this in Photoshop, I might use the
lens flare and/or the
render lighting on multiple iterations of a single base image (in other words, don't apply the effect multiple times), changing the position parameters to make the light source look like it is moving, and output the resulting frame as a gif with a numeric name (frame_0001.gif).
Regarding lens flare and imagemagick: ( http://www.imagemagick.org/discourse-server/viewtopic.php?t=16004 )
Note that in the resulting images they have on that page, there is simply a black background with a white flare. If you create a set of these, and apply them each in turn to a logo image using "overlay" or "multiply" at less than 100% opacity you would probably achieve something that mimics a moving light source.
Bonus points for cast shadows in opposition to the light source.