I suspect that these were intended to be used with the Rubidium standard rather than the inbuilt oscillator.
The reason is that there is an option for this machine to have a real oven installed inside. That is why there is so much empty space.
These counters use a switching power supply from delta (custom hp part number) that is always on. The power button is a soft power button that only toggles power to the counter section.
In the big cavity between front and power supply you can install an 11806 oven oscillator. Those beasts are dead stable. They go on ebay for about 100$ but you need the interface board. (Working on that.. I have a 54131 too and i have an 11806... ) the interface board is a few connectors and two co parators that signal the state of the oven to the counter( temp ok and voltage ok)
On the right hand side , above the fromt end (between front and the bix xilinx ) there is the room to install the third channel. Depending on the freque cy band chosen this module either screws onto the right hand support strut , or it is a block that drops in.
So there you go. That is why this thing looks so empty and is built the way it is built.
The two empty flatcable connectors are to connect the oven and prescaler for channel3.
If you have a standard , like daves rubidium, just hook it up to the back panel ref-in. The counter will detect it , disengage from its built in reference and use the incoming signal. There is some monitoring circuitry that detects the signal falling away and then the machine switches back to its own source.
There is a reason for using 10Mhz. They are the easiest ovens to make and agilent started , back in the hp dayss, to provide an extra input for 10mhz on all their time related equipment ( scopes, signal gens, spectrum analysers etc...) when you buy an oven for a machine it comes with an extra bnc that brings the ref out.
Originally they sold the oven in an external case as well.
Every machine has a ref in and ref out and you can daisy-chain the machines. There is a buffer inside each machine. Of course you incurr skew every time you pass through an instrument.
That is why they sell distribution amplifiers. These are carefully designed to also be phase aligned outputs. You do need to use cables with identical length though !
In my ADSL days i had an agilend gps disciplined reference ( now owned by symmetricom) and such an amplifier. All machinery in the lab was connected to it. We had two network analysers. Prior to connecting them we saw differences between the machines. Connect both to the standard and the became spot on. ( they were calibrated by agilent in their lab using such a standard , so the moment we connected to ours they were performing at their peak.