Just in case you haven't come across the recent RIN report "The role of research supervisors in information literacy" - here is the link. It looks at the role of PhD supervisors in ensuring research students have the appropriate level of IL ability to manage their work and later career. Two online surveys were done (one for supervisors and one for research students)plus 5 case studies. A complex and variable picture emerges (doesnt surprise me..) Supervisors are an influence, even if they dont real;ly recognise the IL concept.A minority do not engage their students in IL. There is emphasis on academic writing and importance of critical thinking which I finbd encouraging. Supervisors are not always aware of the training and help available (surprise surprise). Many admit to being out of date or not fully up to date.
We have an opening here and the recommendations will help this. See here