Like you said, the game manual does not define a Neutral Zone, and thus, scoring bonuses for this “Zone” are not defined. Take a look at criterion #1, rule “a” of the definition of Scored:
Since no point values are assigned for the neutral zone, they will be scored in the only Zone they are touching which has a point value, the Near Zone. The same goes with tape.
Now, a more interesting case which I would like to discuss that you did not overtly mention in our post is “What if a star is wholly within the ‘Neutral Zone’? What is it scored as?” The most applicable rule I find is <G9> (emphasis mine):
I would suspect that since these Objects must have been in the Near Zone to enter this Neutral Zone, they will be scored in the last near zone they made contact within. However, this is worth a Q&A in and of itself
If scoring objects are not touching the tiles in any scoring zone they do not score at all unless it is being supported by a robot or other scoring objects in a scoring zone or a robot that is hanging.
Examples seen commonly in competition that would not score would include the following:
Star remains on top of the fence throughout the match.
Star is under the fence and is not touching the lines or tiles beyond the lines.
A cube is balanced on the fence.
A star or cube is touching both near zones.
A star or cube is being supported by two robots, one on each side of the fence, and the star or cube is not touching the tiles.
Here is one I have not seen:
A very small robot is under the fence not touching either near zone and is supporting a scoring object that is not touching any scoring zone.
No, that is not correct, objects in the Neutral Zone have NOT left the field. Therefore, if they are not touching either alliance’s near zone, they merely do not count as scored. No additional Q&A necessary.