Hi @michael lustig ,
Agree with Andy, if the administrator has disabled automatic replies in your organization(uncheck the "allow automatic replies" in EAC), then when you receive a message from an external sender, the "have server reply using a specific message" rule may not work for you.
In this case, we could first try to send OOF message via Automatic Replies options in Outlook like below(File>Automatic Replies>Outside my organization). According to my experience, if the external OOF setting is not disabled, we could send OOF message to external recipient normally through it.
If the option also couldn't work for you, it's recommended to contact your exchange administrator to check your Auto-reply and OOF setting for your mailbox as Andy mentioned.
Hope that would be helpful to you.
If the response is helpful, please click "Accept Answer" and upvote it.
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.