I seem to remember that the F4K and F4M NWS was slightly different.
The F4M had a linear output, but the F4K was expotential, to reduce its sensitivity around the neutral, (something to to with moving around a carrier deck?)
This could have led to the pilot thinking that nothing was happening until it suddenly 'oversteered'!
Its a long time ago, and I do not have my course notes, so I stand to be corrected on this!
BEagle, you are correct as to the identity of the pilot.