My mistake, the resource files WERE actually copied to target/test-classes. The problem seemed to be due to spaces in my project name, e.g. Project%20Name.
I’m now loading the file as follows and it works:
org.apache.commons.io.FileUtils.toFile(myClass().getResource("resourceFile.txt"));
Or, (taken from Java: how to get a File from an escaped URL?) this may be better (no dependency on Apache Commons):
myClass().getResource("resourceFile.txt").toURI();