Are u asking how to setup DHCP server to pass 2 DNS servers to devices, or how to get a 2nd server running? And what's ur real concern?
If the concern is just some eventual reboot on the server, I don't see the trouble worth it. When I backup my server, I take it down some minutes and apart from new websites I'd open, everything keeps working. Only if it takes longer, Discord goes down. If ur wife complains, ask her to wait 1min while reboot finishes. If it's planned, warn the family first so they prepare themselves.
If u're having some serious availability issues, I'd handle that first.
Internet creators idealized multiple DNS servers aiming at universities, corporations and ISPs providing Internet access to thousands of ppl. In this scenario, if a DNS server goes down, many hundreds will be affected, and they have many server for other purposes, so adding 1 more isn't expensive. But for a home LAN, a single server should be enough.
Anyway, as @yubiuser said, if u add a public DNS server as secondary, it will be used and bypass any blocks u have on ur pihole, so that's not good.
The first idea I'd have is install Pihole on ur router, if it's supported. Then u have 2 devices to fail, 1 of them the Internet provider, before DNS goes down.
The 2nd idea would be a very small and power efficient device, as a Raspberry Pi.
You could put it even on a PC that stays on 24/7, in example on a VMware VM.
If it's rly a necessity, then u must move to more expensive solutions, like subscribing the cheapest VPS on some datacenter.