Big IP APM customized logon background image not loading

There are always multiple ways to do the same thing. I think the problem in your case is that is not internally linked as customization.

Try this way, that I know works.

Go to General Customization, select the access policy, partitions, and then Advanced Customization Images. In image00 select the image you want from the image browser, and copy the final link. Something like /public/images/customization/partition/_general_ui/image00_en.png.

You can then use that link in the Advanced Customization, like this:

background: center repeat-x url("/public/images/customization/partition/_general_ui/image00_en.png");