Elaborate Reset Circuit
On an AVR I can usually get away with shorting the reset pin to ground with a tact switch aith a pullup to +V and a cap if i’m feeling generous. The poor thing probably resets multiple times but no harm. The Z80 is a bit more finicky.
The circuit is based on http://www.z80.info/gfx/z80test.gif with the addition of a Schottky diode between the second inverter and the reset pin. The diode is needed because the power on reset circuit on the cpu board has to be able to pull down the reset pin during power up independent of what this button is doing.