Academic promotion cases are usually made primarily on research income, output and 'esteem points' ie requests to talk at other institutions, prizes etc that promote your research as a 'university of x academic'. Teaching gets nods, but often isnt regarded as 'serious' ..weirdly of course as good effective teaching maximises the availability of good research students and acts as a funnel for continued research ..and therefore research funding. Pastoral administration tasks are even lower..but conversely academics who have strong pastoral skills tend to have stronger research teams arpund them..
What often happens is aggressively careerist academics claim low pastoral abilities or poor admin capability, avoid these tasls or just dont do them, use the time gained to do more talks, research grants and meetin industry or other funding streams, and then be openly critical of academics who arent improving the research profile. These same academics also tend to argue for fewer admin and nom-academic staff to a. increase academic salaries and b. get their internal competitors to do more admin ..so that they can accelerate their relative research and esteem points and keep strengthening their case for salaries.
Just gently mentioning this game will send the most aggressive into gulping paroxysms and declarations of your insanity, so no wonder you are seeking evidence.
Female, and new academics are definitely flattered into taking on pastoral and admin tasks without understanding that its career damaging. VERY strong administrators can have pastoral avtivity as a salary point scorer, and of course pastoral/admin skillcan be valuable in negotiating moves..and can also get you networked and recognised. Weak administrators and heads of dept will struggle. The difficult here though is that academics who are careerist may seek committee positions and openly bully or undermine by voting an administrator seeking to encourage the promotion of more pastoral colleagues..as it undermines their salary and status game (which no doubt they would have plaued differently is pastoral was prized in salary negotiations.
The THES will have articles and Liverpool John Moores have some really good research on patterns in academia.
Use keywords like 'esteem points' 'academic promotions' etc
Athena Swan may have addressed this issue and most subject royal societies will have something abput this in research on career progression
Hope this helps