i dont quite understand your english of 'by the second'. ok well you use Virtual Dub (its free) to crop out the part of video you want a gif of from the entire video, and save it in its own folder as a .tga file. Next in imageready you go to File >>> Import >>> Folder as Frames. use the marquee tool to create the pixel dimentions your gif will take. delete all repeated frames in the animation window. now your gif is set up, you can edit around with making a sig in photoshop and importing it if you havent before, and then extending the gif canvas and placing the sig under the animation.
voila, a gif image sig.
but im not sure exactly what youre asking so... i think youre asking how to make a small video to be turned into a gif... which is simple, the harder bit is making it .tga