Been there. Done that. Key to off, but not lock. Manual hubs in freewheel. Transmission in park. Transfer case in neutral.
Every 200 miles or less: Start engine, put transmission in drive, and run for a minute. This is necessary to lube the transfer case occasionally. It does not splash lube unless being turned by the engine. Put transmission back in park, stop engine, and continue on.
While lubing the transfer case I leave the driver's door open so I don't forget to take the necessary action to continue towing.
I bought my Sidekick with 35k miles on it and sold it with 125k miles on it. No transfer case issues.
BTW the auto is a chevy trans. Chevy parts will fit and are much cheaper than Suzuki parts. Plugs, seals, etc.
