When this condition occurred, I reached under the car and crossed the starter terminals (battery hot to push-on ignition switch terminal) and it worked fine. After a couple more times it was clear the voltage was too low to pull the solenoid into engagement. I ran a wire from the push-on terminal (with a 2 to 1 connector) of the starter to the inside of the car under the back seat to a push-button switch and over to the hot side of the battery, assuring direct voltage to the push-on terminal. When it would not start with the key, I simply reached back and pushed the button and it started every time. Clearly a voltage loss, and myself wanting an automatic way to always assure it would engage properly with the key, I got an aftermarket firewall solenoid from an American car and installed it to provide direct voltage to the starter every time the key was used. Later on (when the warranty claim was turned down on my starter), I explained all of this to the warranty claims person at VW.
Soon after, a bulletin came out instructing people with this low voltage problem to install a Karmann Ghia horn relay in the line at the starter, basically bypassing the front of the car voltage losses, exactly as I had done with the aftermarket solenoid. I, personally, felt the horn relay was a little light duty for this and was far more expensive so I went down to the local auto parts house and bought a "Standard" (brand name), firewall mounted 6 volt starter solenoid to install on my customer's cars. The problem continued into the 12 volt cars and the counterpart in 12 volt was used. Simple to install. It mounts on the transaxle side cover stud or body and is rewired according to the simple copyrighted instructions that come with the unit. When the key is turned, it energizes the new relay and closes it with the normal car voltage even with all of its losses, redirecting the voltage from the battery terminal through the new relay into the VW starter solenoid.
This hotter voltage makes the VW solenoid close properly and spin the starter every time. What was occurring before this solution was the voltage loss or resistance from the battery to the headlight switch, to the ignition switch, through it and out to the starter. This was so great there was not enough power to close the original VW solenoid to energize the starter and make it work.
Probably the most interesting item was when I found out that this is still occurring with newer second generation VW vehicles and many shops do not know what to do. One lady told me she had dealers and independents work on her Dasher, replace the starter and ignition switch, wiring, all to no avail and was finally told it could not be fixed and that she should scrap the car. Most complaints on newer second generation vehicles have come from cars with automatic transmissions because of the added lockout switches. I have had people experiencing this same problem with stick shift cars that have air conditioning.