K4 had a rear engine transverse mounted between rear wheels and immediately forward of hub line, the idea later developed into K7. This drawing for a family car dates from 1956.
During the design of the K4 in 1959 a new idea was patented by Killeen. [details?] The headlamps were specially treated to remain legal but also save weight and help the aerodynamics. They were inside the body, pointing upwards, and the light was reflected from pop up mirrors. This system saved some 13 pounds over an equivalent system with pop up lights. It was subsequently used in both the K7 and K9 designs.
The article in Motor 8/4/67, in which Killeen described K9, states that K4 had then been in daily use for seven years. There seemed to be no other contemporary detail or further record of this car.
[drawing from Motor 8/4/67]
The following photograph was sent to me by Peter Hardy
C. Jackson in 2009 told me that TEK drove a ``Frogeye'' Sprite which had a flat bonnet rather than the characteristic big headlamps. This is the car he used to test his patent and was probably K4, although not quite as in the drawings.