Here's a check lsit based on my experiences with 1951 and 1952 Kaisers:
1. GROUND CABLE: do you still have the braided type? When was it last replaced? If braided, disconnect it from the battery and soak it with a solution of baking soda and water. If it bubbles and kind of sizzles you have corrosion issues. Wiping it down with help but it should be replaced
2. POSITIVE CABLE (to starter motor and beyond): apply the same type solution as used on the ground to the terminal. The cables and connectors may look ok but at 6 volts, good clean contacts are more critical than 12 volt systems.
The fact that you loose lights and everything, not just engine quitting suggest that one of these two cables (more likely the ground cable) are deteriorating. Also, remember that K-F products are POSITIVE ground set-ups like the late 1940's early 1950's Chrysler products.