The Arduino Nano has an external pull-up (probably 10K ohm in chinese clone) from RESET to VCC on the board, which can be a problem.
The 12V reset pulse is short and 10K ohm resistor limits the current to about 1mA, so it may be feasible to ignore.
However, I agree to @westfw's opinion.
But!
Keep in mind that RSTDISBL and DWEN fuses are accessible with ISP and it change ISP to unusable.
The OP may have programmed this.
