Macpro 5,1 mid 2010 cannot boot to Mojave from Mountain Lion?
One possible explanation is that Mojave is on an APFS volume, which Mountain Lion doesn't know about. It's possible that your Mac's firmware also needs updating if the APFS volume is not being shown in the Boot Manager thing (Option at Start).
Seemingly, you have managed to get Mojave booted somehow, so it's not an incompatibility/lack of support for your hardware.
I currently run Mountain Lion in a Parallels VM, on my Mac running Mojave. You might want to consider that, as an alternative to boot-switching.