Electrical – Controlling a 3-pin 12V 3A fan using a Raspberry Pi

Could you post the picture of what's left of the fan, which you have dissected/sacrificed? Does it have a built in controller or motor driver?

If you have an oscilloscope - probe the lines. You can also disconnect one line at a time and see how the fan and the host will react. This could shed some light on the purpose of the lines.

Most fans have only 3 lines: motor+, ground, tach. Without knowing anything else, here's an educated guess about the 3 remaining lines:

PROG is for factory use. Perhaps, the fan has a built in memory (?) for calibration parameters (?).

ENB is a logic level on/off signal. Some times, it can be used for PWM speed control.

IDENT allows the host to identify the fan. On the fan, it could be connected to one of the following:
a resistor, which identifies the type of the fan
a nonvolatile memory
shorted to some other pin, which can tell the host whether the fan is connected at all or not

By far the lowest component count solution to the problem of simulating the TACH signal from a fan is to use a small microcontroller (MCU) that can measure the PWM input signal duty cycle. The PWM signal can be measured two ways with the MCU either by using a timer to directly measure the high / low pulse widths OR by filtering the PWM via an R/C circuit to produce an analogue level that you read into the MCU via an A/D converter channel. The output TACH signal can be generated easily using an MCU timer that is capable of driving a pin. In fact I have even done TACH signal simulation using a timer that generated a periodic interrupt and then let the MCU software toggle an I/O pin in the interrupt service routine.