Wrong chip, additional information

[wvsbsp]

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.

[wvsbsp]

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