Custom Thunar actions are stored in
~/.config/Thunar/uca.xml; copying that file elsewhere will provide a backup that you can restore in future simply by copying it back.
When restoring a file, it’s worth checking to see whether the system you’re copying the file to has any interesting actions of its own (e.g. from new defaults in a newer version of Thunar). Each action in the file is stored as an
<action> XML element; by copying these elements (
<action>, the corresponding closing
</action> and all the text in between), individual actions can be copied, or all the actions from the backup can be merged with the actions of the file in place.