I can't say if it's an anomaly in the Hawkeye or not but I cleared the exact same 'historic' fault code in the ABS ECU many times and each time, the ABS and TC light stayed on. I gave up for a spell and started looking in to what the Hawkeye is able to read and the only fault code the BECM had stored was an ABS fault. I then cleared that but not the ABS ECU and the lights stayed on. So I cleared both the ABS ECU faults and BECM 'ABS fault' before starting the car again. All lights went off as they should after that. I can't fault the Hawkeye really. Any code it's shown me has a full explanation to it and not just a number.
The BECM DOES NOT store fault codes. Other than those already mentioned.