Sounds like you need to replace the wire,... The ECU isn't getting a proper signal from the neutral switch.
The weather could possibly affect the wire itself by shorting or opening the harness based on temperature, vibration whatever ??? Or the ECU may possibly wait for an engine shut-off to establish a full drive cycle ??? (The ECU doesn't really have too much documentation available for it,... it's really kind of a magic box)
The wire replacement really isn't that big a job,... cut the pink/green wire,.. splice in a new wire,... run it through the firewall,.. connect it to the switch,... connect the other wire from the switch to ground (ground it anywhere you want). You could do all that in less than half an hour.
I am going to give this a go after a trip I need to take this weekend. So I should go for the neutral safety first? or the backup light or the Cruise disengage, because all three of these will independently give that code...