Start with the status
Every after-hours call should hear whether you are closed, at lunch, or on a holiday, and when a person is back. Then the agent restates why the person called. 'I understand you want to book a service visit, and the office is closed until eight in the morning.' That one sentence keeps the call from feeling like a machine that ignored them.
Split the work into three piles
Facts you are willing to say: hours, address, what you do, a price range you have approved. Requests you will capture: name, number, address, and what they need. Emergencies you will not guess about: say so, and point them to emergency services or the on-call person you named.
An AI receptionist is good at this split because it does not get tired at 11 p.m. and start inventing. If the fact is not in the notes, it takes a message.
Hand the morning a finished note
The win is not a clever greeting. The win is a message the opener can act on: who called, what they wanted, how urgent it was, and the number to dial. Connect that note to email or a text once the recipient has opted in.