I don't think anybody knows how much of the design was Taylor, and how much Wright. Certainly Taylor built the motor, machining the crank from steel plate (he had only a lathe and drill press to hand, and so had to mark out the crank, drill out its rough outline and then turn the journals).
The original engine was broken up, the crank going to one place the block to another etc. When Orville reconstructed the 1903 Flyer for exhibition (at London's Science Museum) in the 1920s, he had to use many replica or modified parts - and, as no drawing existed, even he couldn't remember every last detail.
Look to the EAA's splendid Sport Aviation magazine for some excellent articles on the latterday building of replicas and the amount of detective work - or even forensic work - involved in getting it 'right'.