Truck not shutting OFF after running in rain..

[JimT]

some things to try, may or may not be helpful...

try disconnecting the batteries. leave disconnected for a few minutes before hooking them back up to ensure any on-board computers/circuit boards fully power down.
maybe a bad relay somewhere? Check all your fuses and relays.
maybe start checking wires for a short? start at the batteries and work your way around, don't forget checking the starter. Could have a (+) wire somewhere feeding power to another circuit?

idk, just some thoughts that come to mind