Just ran across an interesting quirk in System Check:

If you use the "Create" function to re-use an existing Kaseya Agent account (for instance, if you rebuilt a machine and wanted to preserve the history, so you used Create instead of deleting the pre-rebuild identity and letting it re-create its account once it was rebuilt) any existing System Checks will not work until you re-up them.

To do this is pretty easy - just go into System Check, select the machine, "load parameters" for each one, and hit Apply.

But if you don't do this, they just won't do any actual checking; although in the System Check GUI there's no indication that they aren't working, they will look totally normal, and like they ought to be fine, they just won't actually run, trigger, alarm, etc.