How can I fade a GIF in gimp?

this is all i can manage

You have to lower the opacity a little bit for each layer toward the end of your .gif, if you want it to literally fade into nothing.
Are you trying to have only the black outline fade, or the entire image fade out to nothing? You will also have to alter each layer to appear more like the glowing red until you ultimately have the the desired result.
Is this on a transparent background, or is it actually white?

I want the red to pulse, but in a fading manner so that it isn’t as rough as the one I made. It is on a white background.

You’ll have to alter the image so that the red is more prominent on some frames and less prominent on other frames – so that it appears to be pulsing. I really suggest a transparent background for logos, always.