In thin disc kinematic dynamo theory there are two classes of dynamo mode. In the first class, the magnetic field generated has a radial length scale long compared with the short transverse length scale defined by the disc thickness. In the second class the radial length scale is short and comparable to the disc width. The former were investigated in Part I and Stix's (1975, 1978) α ω-galactic dynamo in an oblate spheroid with small aspect ratio, ε, was adopted as an illustrative example. Here we again investigate Stix's model but, in contrast, consider the most readily excited oscillatory dipole mode, which happens to have short radial length scale and so belongs to the latter class. It is shown that, in the limit ε ↓ 0, local theory, which ignores the radial structure of the disc, leads to a critical Dynamo number which is smaller than the actual value by about 20%. The explanation of this discrepancy is the main feature of the analysis.