Likewise, there is no evidence that there is one. I added a 2nd RJ45 port to the blank points on the board but unsurprisingly that doesn't work, you never get a link. It likely is disabled in the firmware, and may additionally also require some combination of surface mount resistors to 'present' it to the SoC. Difficult to trace that as it is a multi layered PCB and I have no datasheet or pinout for the SoC. Packet capture on the ethernet interface that does work yields nothing, regardless of powering on holding reset, pressing and holding reset once booted, etc etc. I've not found a combination that makes any difference. The 2nd ethernet interface doesn't magically spring into life if you power on holding reset, for example.
Next step is to remove that shield and see what's underneath. I'm tempted to order a buspirate too, to lift whatever is in that SPI chip on the underside.