The second gunmen doesn't require a conspiracy to explain. Oswald fired two shots: one in Kennedy's back which did not fully penetrate, and one through his neck which hit Connally.

Then, in the ensuing confusion, a Secret Service agent following the motorcade accidentally discharged his AR-15 in the back of Kennedy's head, killing him.

The agent who pulled the trigger on the ground doesn't even need to realize he had done it; it's possible to accidentally discharge without realizing it.