Can Gradle log or tail the contents of a file as it is being written?

I have a Jenkins build job that uses Gradle to build a Unity3D project. In order to keep track of the build progress, I would like to see as much information as possible in the “Console Output”. Unfortunately the output from Unity3D goes to a file, rather than to standard output. My build.gradle has a task that invokes Unity using ‘exec’.

Is there a script or plugin I could use in Gradle to constantly repeat lines that are written to Unity’s log file onto stdout? I would want this to only happen for the duration of the task that has ‘exec’ in it.