Using the shift function in game is the easiest way to add additional functionality to your existing hats. You just hold the shift button and press the hat. This profile has it already setup https://www.benchmarksims.org/forum/showthread.php?23661-Flounder-s-X52-Pro-Keyfile-DX-Profile-for-BMS-4-33&highlight=Hat+Shift
However, if you are committed to physically adding a button it is doable, but with some work, skills and money. The simplest approach is going to be to nest another controller inside the X-52. Similar to approach in this persons MS FFB mod. https://forums.eagle.ru/showthread.php?t=152723
Here the stick grip is a separate controller from the base. It utilizes a custom control board and it’s own USB cord to plug into the PC.
If you choose to physically add a button, you’re going to need tools to physically mod the stick, like a rotatory tool such as a dremel. Then you are going to need the components for your switch and controller.
Depending on your skill level there are numerous options of control boards to chose from.
Using a Teensy board will require the most level of skill. Basic programing and soldering knowledge will be need to complete a project. The small form factor, low cost and the ability to customize make it a great choice for a DIY enthusiast.
https://www.pjrc.com/teensy/
MMJOY is a bit easier to approach than the Teensy because of the custom software. It is compatible with numerous boards of various prices, including some arduino clones which cost even less than a teensy. https://github.com/MMjoy/mmjoy_en/wiki
Finally there are the leo bodnar boards. Which are the most expensive but require the least amount of knowledge and skill to use. They are basically plug and play. Some boards do not even require soldering. So they are nice option if you just want to get the project done quickly. However they tend to be on the larger size so it may difficult to nest them in the X-52.
http://www.leobodnar.com/shop/index.php?main_page=index&cPath=94
Then you are going to need a hat switch. You can get them from various part suppliers, with cost varying from thousands of dollars to 2 bucks.
Mouser has some otto hats, the ones used in real flight controls for the 100 dollar range. Though they might be to large for your joystick.
https://www.mouser.com/Electromechanical/Switches/Multi-Directional-Switches/_/N-5g2z
Leo Bondnar sell nice small form factor hat too. http://www.leobodnar.com/shop/index.php?main_page=product_info&cPath=85&products_id=210&zenid=e1cf8bf738c902e06736bcfcb384a7ea
And finally there is small low cost one from sparkfun. https://www.sparkfun.com/products/10063
Good luck with your project and please keep update with your progress.
