360 F1 Reverse Switch sending error

Lever breakages are common, but I don't understand the symptoms you are experiencing. The reverse lever is just an on/off switch. If the car is going into reverse gear, the electrical switch in the panel must have been correctly activated (and the ECU has sent a signal to the approriate power unit solenoids and to the reverse relay to turn on the reversing lights).

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Perhaps the initial movement has activated the switch, then the lever has settled away from the switch (confusing the ECU logic)? However, from a safety perspective, I though the gearbox should have gone into neutral if this happened.
There are resistors in the circuit (for selection and non-selection of reverse). Perhaps you could check the resistance across panel plug pins 4 and 5 with the reverse lever in various positions?
i.e. according to the Speedworks FRS wiring diagram above, 4.9k ohms when not selected and 1k ohm when selected.

Experts?

Have you updated the reverse lever to the stronger Ricambi/Hill Engineering one?

https://www.hillengineering.co.uk/reverse-levers

 

If you are in the US, we have those little t-handles here: https://www.ricambiamerica.com/rl01-360f1-reverse-gear-lever.html

They are one of the most common points of failure on the 360 F1 outer gearbox control unit.