Basecamp in 64 bit ready for download:
https://www8.garmin.com/support/download_details.jsp?id=4449
To provide another data point, I also installed 4.8.2 on my iMac 10.13.6 and it also fails to run. It does create a crash log in the Console with the following error (more info available if requested):
*** Terminating app due to uncaught exception 'NSInvalidArgumentException', reason: '-[NSApplication setAppearance:]: unrecognized selector sent to instance 0x60400010b760'
abort() called
terminating with uncaught exception of type NSException
Hopefully, this can be fixed quickly.
Fred