I had to cut a hole on top of the first light fixture box and dig out a little insulation then pulled the switch wire that went to the second light up out of the switch box and stuck it in the first light box and hooked it all up and it worked fine. Now it's wired like this.
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The diagram in reply #31 as of Feb. 7 9 AM is correct.
The diagram in reply #26 as of Feb. 7 9 AM does not give enough detail to indicate a series versus a parallel circuit but does give enough information to reveal the original problem, one light stays on when the switch is flipped off.
The wet cellulose situation is a separate topic that needs to be addressed and fixed (the moisture eliminated).
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.