The neighbor threshold controls the "neighbor numbers" which are found by Neighbor_Search. This can be a little tricky, especially since the neighbor threshold works in conjunction with the similarity threshold. Neighbor number "1" is the nearest neighbor.
The default values in Neighbor_Search are set to a similarity threshold range of 1.0 to 0.7 and a neighbor threshold of 1 to 20. In other words, Neighbor_Search by default looks for the first 20 neighbors and reports all of those which fall in the Tanimoto range from 1.0 to 0.7.
If you wish to guarantee that a certain number of neighbors are returned, be sure to set the lower similarity threshold to 0.0 instead of 0.7. Then, if you ask for neighbors from 1 to 20, you will receive the 20 nearest neighbors, regardless of their Tanimoto values.