This is the best I can do at the minute - it's an extract from an incomplete NES console schematic. So the *RST pin shown here is part of the cpu.

There is another switched circuit (power switch + LED) on the same circuit board which shares the same connection to ground but other than that, I can't find any more exact details about what it's connected to.
I know that joining the solder points of the switch causes a reset - so what I want to do is add an Arduino controlled element in parallel to that to do the same thing.
I'll probably go with the relay option but I'm curious what you all would do.