For the EeePC, install the backports kernel to enable hibernation on lid close.

[config] / buster / etc_files / all / etc / apt / sources.list

deb http://deb.debian.org/debian buster main contrib non-free
deb http://deb.debian.org/debian-security/ buster/updates main contrib non-free
deb http://deb.debian.org/debian buster-updates main contrib non-free
deb http://ftp.debian.org/debian buster-backports main contrib non-free