According to the Brat features website, there is the following feature:
Detailed annotation process measurement
brat can optionally be configured to record the precise time that an annotator opens a document, each edit action, and even the time spent selecting the type to assign to an annotation after selecting where to place it.
However, even after follow the instructions on the tool.conf website, I keep having the error:
Error: failed to initialize annotation log /home/brat/annotation.log: [Errno2] No such file or directory '/home/brat/annotation.log'. Edit action not logged. Please check the Annotation-log logfile setting in tools.conf
I created the annotation file, but the error persisted.