The useful move here is refusing to treat eight as a staffing target and changing what the number is built from instead. With three people, the question becomes which failures are allowed to wake someone at all.
When we set up operations for small teams, we start with a short list: the two or three things that lose money or trust if they wait until morning, usually payments, login and data loss. Only those page. Everything else becomes a ticket triaged during working hours, and the system is designed to degrade rather than fall over, so a failed background job queues and retries instead of taking the app down.
The other lever is buying away whole categories of incident. Managed databases, managed queues and a hosted status page remove classes of 3 AM work that a small team would otherwise carry. It costs more per month than running everything yourself, but compared with the real price of burning out one of three engineers, it is usually the cheaper option.
I would be interested to know how you handle cover when one of the three is on leave, since that is where small rotations tend to break.