No batteries needed when using the external power adapter.
Because the 6VDC battery cells are connected in parallel with the internal power supply 6VDC regulator using a solid state switch made of two schottky diodes. These diodes makes sure that neither power source can feed current into the other, while allowing both power sources to apply current to the printer components.
So only one power source at a time is needed to operate the printer.
That said, there is a catch in that design choice that looks like a design flaw by Seiko Corporation but I may be wrong of course:
Because both power sources have the same 6VDC output, both can actually apply current to the printer concurrently, depending on each actual power capacity at each moment.
Additionally, because electronic components actual behavior differs from the nominal specs between different specimens, the Schottky diodes forward voltage may vary slightly between them favoring one of the two power sources.
The same happens with the internal power supply regulator, a 7806 type, where its output regulated voltage will vary from printer to printer.
The same applies for the batteries.
A good design imho should make sure that when using the external power adapter, the batteries should be disabled.
This really is simple to achieve but Seiko/HP choice was different for reasons that are unknown.
Of course the external power adapter must have good current capacity and low internal impedance to be able to maintain at very least 10VDC at 2Amp.
This is because the 7806 regulators will require at least 3V higher at the input pin than the regulated voltage at the output pin. Additionally the input rectifier in front of the regulator will take around 1Volt.
So any AC or DC adapter will do as long as it can deliver the required consumed current by the printer while presenting at least 10VDC at the 7806 input pin.
I would use a 10 to 12 volt DC adapter, or a 9VAC adapter, both able to deliver at least 2Amp.
The printer consumes way less than 2Amp but the power adapter current rating is related to its internal impedance. The higher the current capacity the lower will be the impedance and therefore the better capacity to maintain the required voltage supply under load.
Another obvious reason to have the batteries depleted while using the external adapter woud be a defective Schottky diode (the one in series with the batteries).
These Schottky diodes tend to fail by presenting high reverse current leakage specially when operating a such high current levels.
I would recommend to have a look to the internal view by Kees here:
http://www.keesvandersanden.nl/calculat ... inside.php
The schematics will tell the full story for those interested in this subject.