It's busted (it's a bug).
It seems the only way Basecamp knows Earth is installed is if Basecamp is installed after Google Earth. It appears that it has to have Earth (just Earth Pro doesn't work).
It works if you run Earth (or Earth Pro) outside of Basecamp. That is some indication that what Basecamp isn't doing properly would be easy to fix.
Interesting! This explains the Desktop vs Laptop issue. On the Desktop I had installed GE long ago then recently installed BC then GE Pro. On the laptop just the opposite GE Pro then BC then GE.
This still isn't fixed; doesn't work whether GEp is open or not.
If GE is not open and running I get the error code "GE is not installed".