The best advice for very busy professors is to find the correct researcher working on their team (scan papers for the one that seems to be coauthor in the field

The best advice for very busy professors is to find the correct researcher working on their team (scan papers for the one that seems to be coauthor in the field you want to ask about). Most of the time it'll get delegated to them either way and if it's interesting enough it'll eventually reach the professors.