A couple of years ago a member on this forum tried to find out the information needed to interface a non-Haas rotary table to the Haas 4th axis in the machine without any success. Haas, not surprisingly, would not provide any information.
I think you will find you are out of luck if you want to do true 4th axis machining. If all you need is indexing not continuous motion synchronized with the other axes you probably can Heath Robinson something together but this does not need the 4th axis in the machine.
An open mind is a virtue...so long as all the common sense has not leaked out.