Why won't 2 switches auto-negotiate (link down) when direct, but will work at 10/100 (or at 10/1000 with other switches)?

I cannot understand why 2 switches won't auto-negotiate or communicate at 10/1000 (1000Mbps) when connected directly together. But they will communicate at 10/1000 with other switches. Can anyone help me?

I have two Ubiquiti EdgeSwitch PoE switches (ES-24-500W and ES-16-150W)

If I link the two directly then the ports show no lights and the web interfaces show "No Link".

If I change the config of one of the ports (either switch) from "Auto Negotiate" to "100Mbps Full Duplex" then the direct link works fine (but not at full speed of course).

If I put the ports back to "Auto Negotiate" but put a cheap unmanaged switch (NetGear GS105) in between the two EdgeSwitches all switches/ports work immediately at full 10/1000.

Things I have tried/checked with no success:

• Checked continuity on the link cable and all cables/patch panels - all pins working and straight through.
• Tried bypassing any patch panels.
• Tried different ports in both switches.
• One of the switches (ES-16-150W) has been factory reset.
• Both switches updated to the latest firmware.