How would I use Exiftool to read or write to the tag:
[File] File Modification date/time
See FAQ #2 (https://exiftool.org/faq.html#Q2).
"File Modification date/time" is not a tag name, it's a tag description. Add the -s (short) option (https://exiftool.org/exiftool_pod.html#s-NUM--short) to see the actual tag name.
It can also be useful to add the -a (duplicates) option (https://exiftool.org/exiftool_pod.html#a---a--duplicates---duplicates) and the -G (-groupNames) option (https://exiftool.org/exiftool_pod.html#G-NUM-:NUM...--groupNames) to make sure you see all the data and what groups they belong to (see FAQ #3 (https://exiftool.org/faq.html#Q3)). My default command to view data always starts:
exiftool -G1 -a -s