we want to use VIM as an unattended linux server.
That means in case of a short power failure the machine must
come back up alone, without sitting there waiting for someone to push
the power button.
How could that be done?
Connecting some pins of the 40-pin header?
Doing some soldering?
Following solutions for your reference: 1) There are two ports can provide the power for VIM: VIN and USB-C, so you can provide the power with two separate power source. Check the Extra Power Input for Vim for details.
In this case: VIM power down only when both of the two power are dropped.
2) There is a power control signal to enable/disable the system power for VIM: PWR_EN, currently, PWR_EN will be 1 when the power AO_5V is applied, so as what RDFTKV mentioned above, the device will boot automate when the power is applied: