Low voltage shouldnt be a problem, I drove couple hundred km without alternator and the turning indicators stopped flashing before ABS light came on (actually only came on after I pressed brake and brakelights sagged the voltage).
It is most likely from old battery struggling during start.
There are no separate sensors for the EBA (maybe an accelerometer inside the control unit?).
The EBA is just done, if I understood it, by blocking the brake circuit to rear axles, and releasing little fluid there as the braking force increases (valves 11 and 18 in the ABS diagram, 12 and 17 stay shut until ABS releases pressure from the wheels).
No kick on the pedal as that is done only when pressure is relieved.
Therefore the only components are the ABS sensors and the valveblock with control unit (and the braking system, but it shouldt affect the errors as Ive had rear pads rusted to the carrier when I bought mine with no errors).
The EBA is propably controlled by wheel slip as I dont see any pressure sensors.
As the error comes only after 10 min drive, my guess is bad connection somewhere.
Run ground cable from abs unit case to the chassis, not ideal but might help if the groundpath is bad (theres diagram for the wiring in pins too).
Change fluid and work the abs to change the fluid inside the pump and valves.
Check the sensor connectors under the rear seats for corrosion (and maybe others too).
Open up the control unit and look for bad solderjoints or dead capacitors?