It would be nice if the supporting manager could add a line or 2 regarding the match. That will likely to be welcomed by the supported manager.
Some minor random gift boxes (like the daily boxes, but maybe with rare chance of greens, low chance of reds or blues and fair chance of money, and in the format like the token-return event) to be given to managers who support other managers, then surely would increase the participation and involvement of managers.
Can even organise some random daily events in our grounds - say PK shoot-outs in our ground’s pitch, ball juggling activity by youth in youth academy (with very minor improvement in %), random player photo-shooting activity in utilities (with increase in morale of that particular player), etc.