Maybe this has already been pointed out, but all John Deere tractor keys are largely the same. So the key provides NO security.
Personally, I would insure it and leave it in an unusual configuration when you are done using it. For example, leave the 2 speed transfer case in gear, as the machine won't start and also, pull or activate the PTO switch if you can on the newest models (mine has the tried and true yellow PTO lift knob which isn't obvious when it on) so the tractor won't start. Also, set the parking brake. Usually, stuff which isn't easy to steal isn't stolen and the stuff which is easy to steal, is stolen more often.
Insure it and personally, I would park the truck outside, but a happy wife is also important.......She will likely fall in love with the tractor too, so she will come around about parking it inside.
Make sure you are 100% clear on what your deductible is on your insurance policy and MAKE SURE the homeowners policy will cover it. Some do, some don't, but you can usually add a Inland Marine rider if the Home owners policy doesn't cover it.
Many homeowners polices now have deductibles based upon a percentage of the total coverage. For example, some are 2% or 5% of the coverage amount. Well, if your home is insured for $400,000, 2% of that is $8,000 and 5% is a whopping $20K, which means the tractor isn't covered.......Many states and policies "updated" their deductibles without a lot of communication, so be 110% certain on this point as I run into people all of the time who didn't know their coverage's were "updated" in this manner.
Just yesterday, our HOA insurance agent "offered" to provide coverage for our private street signs. They cost over $8,000 to install and should one be damaged, its easily $1,500 or more to replace one sign and stone base. (I built the signs, so I know them extremely well....) When I analyzed the coverage, between the property coverage minimum and the deductible, etc, the insurance coverage doesn't make sense.
We can easily "self insure" these as we maintain a large cash balance in our asset account, but I wanted to go through the exercise just to be sure. But to spend $450 for a maximum coverage of $750 per sign makes no sense. Plus the odds of multiple signs being damaged is very low because they are in various locations. Hopefully, the vehicle which might strike them has insurance coverage.
We had two neighborhood mailboxes, which are owned by homeowners, struck by vehicles who then fled the scene. In both cases, security cameras caught the collisions on camera. One was run over by the Molly Maids car and they denied doing it, despite the paint on the stones which matched their paint and included part of the vinyl ":wrap" and the camera image of them hitting the box, getting out of the car when it was "stuck" until they pulled bricks from behind the front wheels on the tiny Ford and then getting in and leaving. Plus, that was the ONLY day they didn't show up at the customers, because the car was leaking coolant when they left the scene and knew it would be noticed.
When in doubt, verify in writing.......and keep a copy.
I insured all of my tractor and implements for total cost replacement, which I think at the time was $42,000. Its actually been increased since more new equipment was added and I think the total premium is about $240 to $260 per year, with a reasonable deductible and full coverage.
Most importantly for me, the coverage isn't restricted to being just on the property, which I had to have........ Many home owners policies won't cover for losses which happen when the equipment is off the home site or they have other limitations. Make sure to ask about these things.......