Wow, that's a really good question - one I never thought to look at. Although we have a regular daily Update Inventory policy that runs, and I can see the entries for that policy running in the jamf.log, of course there are many other items that trigger an inventory update, like most other policies if they are configured to, so that one once daily policy doesn't really help.
I can't locate anything else that would indicate the last time inventory was submitted. Of course it can be gotten from the API, but...
I know this isn't a client side option, but I have a Dashboard item that shows how many Macs that haven't checked in with an inventory update. The policy is set to run once a day. I can also check the list of all Macs with a field for "Last Update" and compare to "Last Update" Screenshot attached.
