can I configure grubx64.efi to look in the same directory as itself, or must it have an explicit prefix & root?

[Avi Deitcher]

I am doing a manual EFI build with grub-mkimage. If I change the drives, or
uuid or labels on my /boot partition, normally I would rerun grub-mkimage
and change the --prefix or --config setting to include an updated
search.fs_uuid or search.fs_label

Is it possible to build the image such that I will not have to rerun
grub-mkimage? Can I include those in a stub grub.cfg colocated in the same
partition and directory as grubx64.efi, and tell it to look next to it for
the grub.cfg, so that a change in drives/partitions/labels/uuids means
updating just the text grub.cfg and the image will continue to wor?

It might be easier to change my stub grub.cfg, rerun grub-mkimage
--config=updated/grub.cfg and reinstall, but I would like to know if it is
an option?

Thanks
Avi