Thank you for the follow-up.  I myself have used Cocoatech's Path Finder – I think it's the original Finder replacement, for 20 years or so, and have never seen this issue with apps like BookMacster which have built-in helper tools.  It might help to give the ForkLift developers the path to BkmxAgent,

BookMacster.app/Contents/Library/LoginItems/BkmxAgent.app/

Yes, I think you've found the problem there.  As I recall, downloads from the internet are quarantined by macOS adding an extended attribute titled com.apple.quarantine to the file's metadata.   I think that attribute is removed when the user manually drags the file, directory, or package (macOS apps are actually a package which is a directory with an extra bit set in its metadata) into the /Applications folder.  I'm not sure, but I think that if you installed BookMacster.app into /Applications by any means other than a Finder drag, the quarantine is not removed.

The fix may be as simple as dragging a non-running BookMacster out of /Applications and then back in.

If that does not work, the answer in this Q&A in superuser.com (including the Comment by AKX) should work.  The path to the BkmxAgent package is:

    /Applications/BookMacster.app/Contents/Library/LoginItems/BkmxAgent.app/

and although I don't think you'll need it, the path to the executable is the following three more appended to that…

    Contents/MacOS/BkmxAgent

Please et us know what you find, and also if you have any idea how the installation might have gone wrong.

• Activate Finder.
• Click in the menu: Go > Go to folder…
• Into the small text field which appears, copy and paste the following path:

    ~/Library/Logs/DiagnosticReports/

Do you see any files named with BkmxAgent in there?  If so, send to me.

Finally, do you run any anti-virus software on both of those computers which might be too aggressive?

Strange error, even stranger that it would happen on two computers, but I can't imagine how the two could be connected.  Start with one computer.  Maybe you've got a hung BkmxAgent.  Switch syncing off and verify that all BkmxAgent processes disappear.  Detailed instructions below…

• Activate Finder.
• Click in the menu: Go > Utilities.
• Launch the application named "Activity Monitor".  A window will open.
• In the top right corner of the window is a text fieod for filtering results.  Type "Bkmx" into that field.  The list should collapse to show only any "BkmxAgent" processes that are running.
• Select one and click the "X" tool in the toolbar.
• Confirm that you would like to "Quit" the process, and if that does not make it disappear, "Force Quit".
• Repeat if more than one BkmxAgent is running.
• Activate BookMacster.
• Click in the menu: BookMacster > Reboot Sync Agent.
• Verify that a new BkmxAgent appears in Activity Monitor.
• Click in the menu: BookMacster > Reboot Sync Agent again.

Does it inidcate success?