Re-reading the above I'm tempted to delete it and start again, but who knows, someone may have read it. Let me simplify a little:
1. What is the idea behind weekly/monthly/all_time division of members?
2. Precisely what actions cause a member to be promoted to weekly?
3. Can the "up to 24 hours" delay be removed please (if the divisions are retained) since anyone going to rely on the divisions can easily force an update by banning some random non-member (Erik is the usual example 
) and un-banning him afterward, which will force a second (and unnecessary) update
4. I would like at least the following to constitute activity:
• Being registered for a team match when it begins
• Casting a vote in a vote chess game
• Making a forum post
• Sending an invitation or any other activity restricted to administrators only down to and including editing the club's profile
5. While I'm wishing, I'll wish that posting a note be recorded separately; for some teams that is significant and for social chatty teams it may not be. Indeed, in one club it makes one nuisance look active whom the club would be better without. (So why not kick or ban him? Because while I would never invite that person to a club, arbitrarily kicking people out of your club is a very fast way to destroy morale. A medium fast way is to let nuisance chatter take over your notes. Tricky. Dealing with people is always tricky.)
Two teams I help administer have substantial "dead wood".
My first place to look to identify it was via the club members endpoint, which splits club members into three groups:
Now that's all well and good, but if I have a smaller team and value players who participate in "important" team matches (e.g. TMCL) they may spend a lot of the year in #3 ("all_time") if:
I assume here that making a move in a team match game does not count as activity; it would be good to have more explicit documentation of exactly what does (and does not) count as "activity" but it is practically a side issue, as my hypothetical "important" match player will sometimes have an opponent who doesn't actually play (closes account or times out).
I still value my "important match" player so to find if they are active or not, I need to:
It is clearly possible to do both #1 and #2 immediately above, with #1 being trivial and #2 requiring some programming (or work with the JSON capable utilities perhaps).
If all_time/monthly/weekly were better defined it would have some value, perhaps.
I am interested in what was the last time an administrator did something, when people post to forums and even when people post notes, which is one thing which is documented to bump their activity level. Especially as there are no endpoints to such non-public data as clubs' forums when a club has made those forums private, as most do.
I started out writing this post thinking I would propose that the division of weekly/monthly/all_time be scrapped. Instead I am thinking I would like it to stay (even if it is only updated each 24 hours or on some specific events) as I can work out without api.ches.com if I can't find matches they have played in what someone has been doing, by asking them if necessary.
*I have seen members purged from clubs for not being active on chess.com (the easiest measure until recently) from as little as one month to as much as eighteen months, with the justification for the latter being a one year sabbatical with some time either side.