Spontaneous reboots - how to debug

Currently I'm running a DEC740 from Deciso (x86) with OpenWrt trunk and it sporadically reboots.
I thought it might help to enable remote logging, but it turns out it doesn't transmit any relevant information.

What would be the best approach to debug this?
Since the device is headless I'm thinking to connect a serial cable and somehow record the output in order to be able to scroll back to when it happened.
As I have plenty of hdd space could I also enable persistent logging to disk?

What do you think?

Install kmod-pstore and kmod-ramoops and see if something ends up if /sys/fs/pstore maybe...

According the vendor specifications, your device seems to have a console port (mini-USB?) - that would be the next step -beyond pstore- for trying to gather logging information.