I wondered if there's a way to extend my "online" timeout (separately from everyone else) so my staff online entry hangs around for longer after my activity has stopped?
Or maybe tweak it on a usergroup basis for admins/mods?
Problem with having staff show online for longer than they are is that if something happens on your forum which requires staff interference and they're showing but not doing anything about it, members start to question why.
Rather than have staff showing online for longer in the Staff Block, why not consider removing the block altogether?
Members still be able to find out who are Staff from the Members tab (and a reminder in the Site News will point this out to anyone who hasn't found this, such as Tapatalk users who have finally found the full site )
This way, it's not glaringly obvious which staff are currently online and possibly more importantly, which staff aren't on the site.