The markings look like an Atmel part (it starts with "AT", which is common for Atmel parts). Given the size of the chip and context which you provided, I figured it was probably a serial EEPROM. Looking through Atmel's serial EEPROM datahsheets, your mystery chip is almost certainly an Atmel AT25128B-SSHL SPI EEPROM, which matches your chip's product ...
You would probably need some expensive scanning equipment. It is possible you could get old equipment that is being discarded but that would be rather difficult. Then you would probably need to write software to handle the output of the equipment as you most likely wouldn't have a license for the accompaning software unless you nabbed a complete system ...
There are comprehensive tools that can do precisely this. Part of the software that comes with them allows you to place part numbers between pads and have the circuit diagram automatically generated for you. Unfortunately, they're likely to set you back a fair bit of cash.
An alternative is to use corrosives and sharp implements to manually split the layers,...
My guess is that the protocol is standard, using a non standard protocol between two devices involves using bitbanging which is not very useful.
Let's assume then that the protocol is standard.
It's not SPI, SPI needs 4 lines To work. I2C needs two, RS232 needs only two.
I don't know what the third line job is, maybe it's used for trigerring/synchronization ...
You can try this:-
All Data Sheet
(sorry this won't allow me to post more than 2 links, you can refer wikia page for other sites like All Data Sheet)
Identifying and deciphering the part number Deciphering a chip's part
number is a very ambitious process and most of the time, typing the
whole part number in a search engine gets you nowhere.
It may be possible. Based on the data sheet you posted, you need to see if Pin 9 is tied directly to ground, or can be controlled by the CPU. If it can be controlled, the chip can be re-programmed.
If Pin 9 is tied to the CPU, you may then be in the realm of trial-and-error to see how to control that pin.