OK it seems the micro switch on top of the 4th contactor is working. Work this way around. Open up the door and bypass door switch. Jack up the wheel (door), making sure the wheel does not touch the floor. Then try to operate the twist grip to go into speed sequence. As you mentioned, there is 1st and 2nd speed, that means either the 1st or 2nd contactor will close followed by the 3rd contactor. When you go into the 3rd speed, make sure the 4th and 5th contactors close too. If not then there is no power supply to the 4th contactor. You can also measure the brown wire on the terminal board situated at the door side and should have about 12vdc. This brown wire supply positive to the 4th contactor coil. As such you should be looking at the mast switch and the rabbit switch. Charger output is 12vdc and 10 amps.
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