External drive Mojave installs unaccessible from Mavericks I've installed Mojave fresh, direct using an Apple-downloaded installer 4x now on 2 brand new, freshly formatted Seagate 2TB drives as well as a partition on another reliable non-Seagate drive. Drives were formatted Mac OS Extended journaled and GUID and connected directly to usb on specced-out Mac Mini 2012 running Mavericks. In all cases install was smooth and ended with booting to fully operational Mojave installs on external drives. All good so far.

Restart as-is ie back to fresh-installed Mojave on external USB drive and all good, boots to external Mojave with Mac Mini on-board OS and files also visible as expected in Finder.

Reboot to the original on-board OS (Mavericks) either by selecting in prefs>startup disk or by shutdown and disconnect/reconnect external drive and the new Mojave partition doesn't show as an OS or on the desktop or anywhere. In Disk Utility it's now greyed out and renamed to disk1s2. A 2nd non-OS partition on the same external drive shows up as normal, just the Mojave partition has gone AWOL and doesn't appear in prefs>startup disc either.

I tried using Disk Utility to check/repair after this all happened. 'root' external disk shows no problem, non-OS partition shows no problem, Mojave partition is greyed out and has random generic name disk1s2.

User passwords and computer name are all different.

The output from Maverick's diskutil list disk1 command for an external drive is shown below.

/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *2.0 TB     disk1
   1:                        EFI EFI                     209.7 MB   disk1s1
   2: 7C3457EF-0000-11AA-AA11-00306543ECAC               1.0 TB     disk1s2
   3:                  Apple_HFS spare B                 999.5 GB   disk1s3
The simplest way to boot back to Mojave would be to reboot the Mac and immediately hold down the option key. This will invoke the Startup Manager. Select the Mojave startup disk. Next, click on the arrow below the icon to boot Mojave. If you wish to make Mojave the default, then hold down the control key before clicking on the arrow.

Apple a recently added new instructions for using the Startup Manager. These instructions can be found on the Apple website: How to select a different startup disk. 

While it is technically possible to select Mojave directly from Mavericks, this would involve installing a third party boot manager such as rEFInd. Unless you intend to change operating systems often, such an installation would probably not be worth the trouble to pursue.