AC43.13-1B is written for those maintaining part 23 aircraft. Back in the CAR 23 days, the FAA recognized that aircraft couldn't fly without oil in the engine, so it was included as part of the empty weight. When the CAA became the FAA and CAR 23 became Part 23 under the FAA, the standard changed to not include oil in the empty weight. I would guess that was a change favored by manufacturers so they could tout a lower empty weight. So, your older plane certified under CAR 23, like a Cub or Champ should have the weight of the oil included as part of the empty weight. Newer aircraft certified under Part 23 don't include the oil as part of the empty weight.
That's the definitions as best I understand them. To me, a typical gasoline engine requires a sump full of oil, so the oil should be included in the empty weight. The plane I completed 18 years ago, I left the weight of the oil out of the empty weight. The two I have built since included the weight of the oil as it doesn't make sense to me to leave it out.
-Cub Builder