Can a Wyze base station be switched to a different wifi?

I can’t seem to switch my base station even if I plug it in to the alternate router.

That is because you set the base station up with a specific router with an SSID and password. If you want to set it up on a different router change the SSID and password on the alternate router to match the original router used for set up. Either that or delete the base and camera/cameras from your account and set it all up again on the new router. Or you could set up a guest network on the alternate router and use the same SSID and Password as the original router. It’s a security thing.