I agree RBM that the jumper is for sharing a common hot feeding
each . The white and black are being used as switch legs feeding in
and out from the hot at the fixture - thru the switch - back to the -
black side of the fixtures . Fixture # 1 obviously has a neutral up at
it that it uses . Your not sure abou the other neutral ? But your also
not sure what is in the box up at fixture # 2 ? I am assuming you
haven't even opened it yet - because you claim to not have easy
access . I'm sure the neutral for # 2 is up there for fixture # 2 .