You could fit a headerless teensy, or single use (deadbug/freewire) ATMEGA16832TQFP flashed with some basic PWM instructions and a simple toggle button to cycle brightness modes. couple decoupling capacitors,16mhz xtal, and 60+ LEDs w/ 60+ 470ohm Resistors and you should be good (although, I would bring in a secondary power supply to the ATMEGA, but you could possibly piggyback. Although you might need to provide a secondary 5v-3.3v regulator and power from the usb/ps2 port or the LEDs as well because I wouldn't trust the ATMEGA168's internal regulator for that many LEDs. Also, might want to break the LEDs into Multiple Parallel Matrices rather than just have them all in series on one GPIO (8x8?).
To make it a little more flexible though, you could use an ATMEGA42U4 and latch on to the usb header in the keyboard and have an application on your desktop to adjust the brightness via a serial(usb-serial, not actual 9-Pin DSUB COM) interface..... (This is all on the assumption that the previous mention of the LED holes without traces is correct, since I can not see the PCB, I can't be certain.)
And obviously, it also is completely dependent on what type of LEDS you choose and their power requirements (12v, 5v, 3.3v, 1.8v). So the 470ohm rating is just with the assumption average power requirements is roughly 160mW, or 410ohm