Do you have a schematic for it? just to locate the two GLU pins.

also, which pins (on the LTC1040CN) should I probe?

EDIT: the switches are indeed connected to the two pull-up resistors (on the bottom of the PCB), those resistor are connected to VCC (+5V?, I checked continuity using the VCC pin on a 74-series logic chip present on the board).

The caps are connected to the switches (for debouncing?),

if I got the numbering right, reset goes to the last pin of the GLU, while NMI is on pin 26.