Hello @lp1,
I've setup multiple type of automations in airtable, till now I've not found that type of behavior in automation.
Within airtable automation it's not possible. If any of the normal automation is off then there are no possibility to execute it. You can just test it while your on editing mode.
Even Webhook based automations are also not executed without its turned on.
I recommend you to please clear your browser cache and then check it.