Kneeling, the doctor touched his hand to the victim's throat in a manner that would have been entirely convincing

had be been checking a body for a pulse. Since the patient's eyes could be seen fluttering in his head such checking seemed entirely redundant.

Hi, I am looking for the syntactic description of the verb chain highlighted above . Thanks.
I believe this is misquoted. It's "had he been checking", an inversion of "he had been checking" used to mean "if he had been checking". The verb tense is "past perfect progressive".
Dear Sir, I was guessing but I wanted to make sure. Thanks anyway.