When I was transferred overseas I drove my truck to Tucson (nice dry heat), did a oil change, filled the tank with premium and added fuel stabilizer, and rented a covered stall in a storage place. Put it up on jack stands. Dropped the tire pressure by about 5psi. I left a couple windows slightly cracked for venting. Had the insurance company tell me what kind of coverage I needed on it and went with that.
When I came back a few years later it was paid off. Put in new plugs and put it on the ground and drove away.
Its your choice. But also keep in mind other than the main roads in most European countries, trucks don't fit real well.
A couple of other factors to consider. The fuel overseas when I was there was not unleaded and insurance costs were astronomical.
You'll have a license plate or other tag/decal that will tell everyone you're an American. But they will have to look for/at it. Driving a big American truck will make you stand out and that is not a good thing. Not only in regard to terrorists but also insurance scammers. If people know you're an American, they WILL arrange to get hit by you. I've seen it happen.
If you've got a sponsor over there, do some checking. You will probably be able to pick up a used car to drive while your there and sell it to a GI when you're ready to leave for probably what you paid for it.
When I was in Okinawa that's exactly how it worked for me. The car was a turbo-charge Nissan screamer too. Sold it to my new OIC when I left.
We have quite a few European members here. Maybe it would be worth your while making a post with a subject like "European Member I Need Input" or something like that.
Not trying to tell you what to do, just offering food for thought based on my own experiences.
"A veteran - whether active duty, retired, national guard, or reserve - is someone who, at one point in his or her life, wrote a blank check made payable to The 'United States of America', for an amount of 'up to and including my life.'"