In February 2020 I heard from Tomas who was using a t510 (running Debian) as an offsite backup server. Interestingly he was running his t510 from a 12V supply (rather than 19V) and had also built the power supply into the t510's case.
To a degree I'm not surprised that the t510 runs off 12V. Modern switching voltage regulators can work with a wide range of input voltages. One thing I wonder about is the serial port. There is a possibility that the RS232 driver chip might be powered off a derived 12V line and exactly how that behaves from a 12V input supply I don't know. If you're intending to use the serial port in your application you may need to check this out.
I have (briefly) confirmed that my t510 does indeed boot and run Tiny Core Linux when powered from a 12V supply.
In December 2024 I had an email from Антон who provided a link to a Russian article on modifying switch-mode power supplies to change their output voltage. Maybe something for the more adventurous (and suitably skilled) to try?
Tomas sourced a small power supply (12V 2.5A)
from AliExpress. It is 3.7cm x 7.7cm in size and cheap (~1UKP or $1.30). The small size
is important as....
...the PSU is located in the 'secure' USB compartment in the t510 housing. Note: This
does have mains voltages on it and you need to pay due care and attention to how it is
mounted to and insulated from the metal chassis. Also it will generate some heat so
ensure there is adequate air flow around it.
The 12V supply leads are connected to the t510 circuit board by the power socket.
Inside view of the complete t510 file server.
I did try searching AliExpress for "19V switching power repair". (You need to use "repair" or "module" to get the bare bones style of PSU). The 19V was effectively ignored and virtually all the results were for 5V, 12V or 24V supplies.