Wire trick time!
Let's take a peek at the UART communication line of the calculator's internal circuit.
Using 'USB to Serial converter' and 'Terminal program', can saw a communication packet being sent each time when pressed the numeric keypad.
When send packet in reverse using Terminal, it behaves the same way as pressed the keypad.
0:00 Wiring
0:12 Take a peek packet
1:10 Control calculator using another terminal