furrtek
Wrong chip, additional information
The DC-motor regulator chip is a BA6220 (not BA6620). The datasheet is available here: http://pdf.datasheetcatalog.com/datasheet_pdf/contek-microelectronics/BA6220.pdf I found a very good explanation of the function of these motor control circuits. https://www.precisionmicrodrives.com/content/ab-026-sensorless-speed-stabiliser-for-a-dc-motor/
A complete different idea: why not omit the whole main circuit board? Just rebuild the motor-control circuit (you get the BA6220 for a few cents on Aliexpress or Ebay) and control the printhead directly from an arduino controller. With a ESP8266 you could even build a wireless label printer :-)
To lower the price for the labels, you get cheap replacement cartridges on Aliexpress, which do work properly.
You also find service manuals for the P65 which show the timing of the communication to the printhead module. https://www.manualslib.com/products/Brother-P-Touch-65-2793398.html