Is it a good idea to have a secondary person on call for production operations?
I can't imagine having only one person on-call at a given time. There are several reasons that the primary person could be unable to handle an issue - perhaps they are unable to receive alerts, they have limited Internet access for a period of time, they or a family member could be ill and they are unable to work yet the on-call rotation hasn't been updated yet. If you have agreements in which you need to start and/or resolve issues in a specified amount of time, having only one person to get notified and start the work seems very risky.

Having a clearly-defined second person is also useful if the first person gets stuck. There's someone who knows that they are on-call and is hopefully doing the best they can to remain in communication and have access to the resources they need. It makes it easy to know who that person is and get help when it's needed outside.

However, if you are having "too many issues going on" or have so many on-call issues that the primary needs to "focus on more critical issues", that would seem to be indicative of poor product or process quality. Situations that require someone being called off-hours should be rare and not the norm, and simultaneous issues should be very rare.

Of course, this is likely to vary by system. Companies that operate at scale of Amazon and Google are vastly different than a B2B service with half a million total users globally who use the system during working hours. Larger, more complex systems with a need for greater up-time are going to have more people on call and shorter thresholds before proceeding down a call tree than smaller systems.