[bionicmerlin]

The pictures aren’t much help but on the diagram assuming that’s the correct one for your clock , it’s very clear that the motor is connected to the mains side of the transformer. . Does the mains go to the tag strip first ,then to the transformer. Also its in parallel with the neon . Possibly the neon is connected to the tag strip as well. It shouldn’t matter what way round the motor white and orange wires go to the mains .
Your probably ok with your oiling , in a ideal world I try and get all the old oil cleaned off before applying fresh. That’s not always easy and probably abit over the top.
Some of these clocks have a internal fuse but yours appears not to have one . Just make sure you have a low amperage fuse in the plug top . We used to use 2Amp but I think you can only get 3amp now. Andy