Program different kinds of software. "On call" isn't a thing for some kinds of software. If it's not deployed to a production server, it likely doesn't have software engineers on call.
I'd aim for a giant bank / financial services company. Some still mandate dedicated Ops/Prod Support teams. It can definitely have it's drawbacks, but you're very unlikely to ever be called out.
Not an answer to your question but I used to keep the on call money in a separate pot. Then over time I would buy something fun from the pot, like some new tech. I found this helped me.
If you can stand the pay and working environment, government (local or state in the US) internal non-safety critical app work may be the safest thing -- you almost never have customers in multiple time zones, or with working days or hours significantly different from your office's that need support.