https://specifications.freedesktop.org/basedir-spec/basedir-spec-latest.html

$HOME/.config
$HOME/.local

Those are promising places to look for X logs

(|N/A:default)cbbrowne@cbbrowne2 ~> find -name "*X*.log" -type f
./.local/share/xorg/Xorg.1.log
./.local/share/xorg/Xorg.0.log

--
When confronted by a difficult problem, solve it by reducing it to the
question, "How would the Lone Ranger handle this?"