I have been using the Pi since the beginning and Linux for far longer but I have no idea what you mean by the "the RUN connection on a RPi board". My research with google did not turn up anything interesting.
What on Earth are you talking about?
I suspect you may mean this reset line labeled RUN that appears at a hole on the Pi boards labeled "RUN". https://raspberrypi.stackexchange.com/q ... berry-pi-2
For remote systems like this I have used the on board watchdog facility to good effect. https://www.domoticz.com/wiki/Setting_u ... i_watchdog
A crucial thing to have for such a remote system is a root file system that cannot be corrupt on random power downs and resets. To this end ensure your root file system is mounted read-only. There are many discussions about this here on the forum.
Of course if your Pi is part of a system that includes GSM modems or whatever you may want to protect yourself against those getting stuck as well. In which case a little 8 bit micro as an external hardware watchdog that can power cycle the whole system is a good idea. Or other hardware solution.
I have also seen systems where the hardware logic itself would get jammed and a simple reset whilst powered up did not unjam them. Again that might call for a watchdog that can power cycle.