Hello again poenwl!
Unfortunately fixing your z-axis limit switch to either a high or low input won't work - the homing cycle requires a change of state to operate.
The right way to do this for a two axis machine is to disable z-axis homing in software, to do this you need to change a couple of lines of code in the config.h file of grbl, then recompile your custom version of grbl and flash it to your Arduino.
In config.h, comment out the following two lines:
#define HOMING_CYCLE_0 (1<<Z_AXIS)
#define HOMING_CYCLE_1 ((1<<X_AXIS)|(1<<Y_AXIS))
then add in:
#define HOMING_CYCLE_0 ((1<<X_AXIS)|(1<<Y_AXIS))
Instructions for compiling Grbl can be found here.
Hope this helps!