To hopefully give some slightly more technically precise answers here:
We have no explicit option for "idle timeout" that would do something like prompt us to send a DELETE message to a non-meraki peer that would tear down an established tunnel.
For IKEv1, the tunnel will be torn down after the lifetime expires, unless interesting client traffic has already prompted a rekey beforehand, or, if DPD is in use, after the peer stops responding to any R-U-THERE (yes, that's really what they're called) packets for too long.
For IKEv2, owing to changes in how the protocol operates, DPD is mandatory. However, by default, we won't send any DPD informational messages unless there is no client traffic traversing the tunnel (but will still ACK any DPD messages we receive from the peer in question). Otherwise, the same rules with lifetimes continue to apply, though it's also worth noting that since IKEv2 no longer requires equal lifetimes on each end of the tunnel like IKEv1 did (again, this is a change in the protocol itself, not one we forced), you may see a tunnel getting torn down as a result of a DELETE message getting sent by one peer to the other, rather than being logged as a lifetime expiring.