Well, I have found two main ways to sniff and decode NRF24 communication:
Both methods comes with detailed instructions on how to perform promiscuity scan of NRF24 addresses (the hard part), allowing to find the specific address of the keyboard to reverse. This task is not trivial since the base address length can be up to 4 bytes, which leaves us with too much combinations to brute force.
After the base address is found, and a solid sniffing channel is established with the keyboard, it is relatively easy to extract the XOR encryption key used to encrypt communication between the keyboard and the lost dongle. With the key it is almost trivial to reconstruct the original communication between the wireless keyboard and the missing dongle, and there are more than enough ways of achieving that, one even includes using Arduino with DFU upgrade.
An interesting fact to note is that the XOR encryption key can be easily extracted once the NRF24 base address is established, since HID packets usually contain many zeros - 0 - and XOR between the encryption key and zeros reveals the key, sometime more than once in a single packet! :) )
There is also a porting of the Goodfet to arduino, but I couldn't find good examples on how to use it properly on an Arduino based MCU.
It is not only the number of pins used to read a keypad matrix that matters. One thing to consider is the number of crossings of traces, i.e. the number of vias needed. Each one needs a hole to be drilled and this process was not as much automatic in the seventies as it is today. But, this is not the major point here:
A 4x5 matrix following the geometrical layout of keys is complex to decode in the processor. While this is a trivial thing to do in todays CPUs, pocket calculator always had and still have very simple processor architectures. At that time, mainly because of the price. Remember, the computer processor of 1971 was the Intel 4004, 4 Bit and 100k instructions per second and it can be assumed that the chip of this calculator (I was not able to find a datasheet) is less powerful.
The table @futurebird created while inspecting the circuit looks like there is a total mess of connections. Actually, this is not true as we see by simply rearranging columns and rows:
H F G B D
A 1 3 5 7 9
C 2 4 6 8 0
E . % C
I * / + - =
Here we can clearly see the intention of the developers: All the even numbers share pin C, all odd ones share pin A. This makes decoding a key press to form a number in memory as simple as possible: On the silicon there needs to be just a "5 inputs to 3 bit encoder" to get bits 3..1 of the resulting digit in binary representation while the lowest bit is set or cleared depending on whether line A or C was active.
In the same manner, all operations can be detected by checking line I and the more special ones on input E.
Compare that to decoding a digit from the basic 4x5 matrix: Here there are 7 inputs to be checked to retrieve 4 bits of the resulting number. It is obvious that this look-up-table consumes more space on the silicon fabric.
Using this matrix connections, the expensive features on silicon are kept at a minimum, while putting a little thought in carefully planning the structure of the matrix and a little effort in designing a PCB matching the intended connections which doesn't add a lot to the overall costs of the device.
Best Answer
It may or not be used by your specific tv. But it is not uncommon for a pcb to have a populated but unused internal connector. The same board may be used in multiple model tvs or with different but equal modular parts (power supplies, output boards etc) so they use a general board. Design once and use in modular fashion as needed.
It could also be a debug or test interface.
Good luck.