I've never even seen a T500RS, much less poked around inside one, but electrically there's effectively no difference between the normal buttons and a SPST normally open switch that you could solder on. Sure, the resistances will most likely be different but the IC the buttons are wired to are voltage driven anyway so that won't matter.
As for where to solder the switch on, open the wheel up and follow the traces from the button you want to use to a point you can solder to easily - a multimeter with a continuity beep function is a good tool for that. Solder it on with multi-core 24AWG wire, give it some slack, hot glue it near the solder points, find or make a hole in the case to run it through, hot glue it again at that hole to prevent accidentally yanking it out of the case then solder the other ends to your switch - make sure it's either SPST (single pole double throw) push to make (aka normally open) or SPDT (single pole double throw) where you only wire the common and NO (normally open) contact, leaving NC (normally closed) unsoldered, depending on what kind of switch you can find in the shape you need - microswitches will probably be your best bet but they're typically SPDT.
If I get time later I can make some drawings that demonstrate the differences between switches and how to wire them if you need that.