Discoveries of Vedanta are not a matter of belief but of reality. This explains why ethics cannot be linked with scientific reality. What Tilak has done is to take the latter as the basis for the former, may be out of his keenness to find a basis for ethics in Indian philosophy which, by common consent, lacks ethical deliberations. This is mixing up willed cognition with true cognition. Values that make ethics are a matter of will which changes from time to time, place to place, and society to society.
Scientific reality is the same for all.
In the events that follow BG, he has behaved in the same manner as any normal warrior would. And Krishna, too, who has played all tricks a practical man would. If events in the subsequent story are to be taken as indications, there is every reason to believe that the two were as normal as any man of the world. The only possible conclusion is that they were not enlightened in the Vedantic sense of the term, in case we treat the events and personalities associated with BG as historical. Stories in philosophical works are just frameworks meant for providing an occasion for the presentation of the teaching.