I do have a partial solution. When my own __DIE__ handler is being called (but I think I cannot guarantee that), then the runtime error will have no caller() info.

So, when the eval'ed code does not mess with the __DIE__ handler, I can differentiate the three:

   my $cause = 'PARSER';
   eval { local $SIG{__DIE__} = 
            sub { $cause = caller ? 'EXPLICIT' : 'INTERNAL'};
          $do_something();
   };
   print $cause if $@;
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Now a solution without the volatile __DIE__