I have created drivers for Brother Printers where there is not an already made PKGBUILD in the AUR.
The .deb method worked best for me. Make sure that CUPS is enabled on your system:
systemctl enable --now cups.service
systemctl enable --now cups.socket
systemctl enable --now cups.path
Have a look at the Arch Wiki:
https://wiki.archlinux.org/title/Packaging_Brother_printer_drivers
Additional info: