So far as I was able to tell, EQ is looking for files which I am not using, and am not referencing in my EQUI_Animations.xml file. In my case, they are files EQ WOULD be using, if I was running with the default UI. I solved this problem, by editing my EQUI_Animations.xml file to include references to these textures which I do not use.
I use the T. King spellbook textures, which are named differently from the default spellbook textures ( ie: "tkspellbook01.tga" instead of "spellbook01.tga" ).
I add this at the bottom of my EQUI_Animations.xml file.
<!-- Default Texture Items I Don't Use, Listed Here to Shut EQ Logging Up -->
<TextureInfo item = "spellbook01.tga" />
<TextureInfo item = "spellbook02.tga" />
<TextureInfo item = "spellbook03.tga" />
<TextureInfo item = "spellbook04.tga" />
I suggest looking through your custom EQUI_Animations.xml file, to see whether all of the "default" texture files are referenced; add similar "empty" entries for those default textures you do not use, and which are not mentioned in the file.
these references could also be a file that you are not use to seeing, but the UI is looking for.