I am surprised that theft isn't a named peril in your state. Theft is one of the named perils in my five states. We have 16 named perils in some and 17 in others. Theft is definitely one of them. There is exclusionary language under the theft peril that defines when a theft would not be covered, but I just read each of them again and we do not have exclusionary language for a tractor at the dealer. I see it defined as a theft from a known place when it is likely that a theft has occurred. That is easy enough. It is at the dealer and it is gone. Then you have to file a police report. That is easy, would be done anyway. It isn't a trailer, camper or watercraft so it doesn't matter that it is away from the residence premises and it isn't at a residence owned, rented or occupied by you while you're not temporarily residing there, so those don't apply either.
The policies I am familiar with would be adjusted something like this.
1--Facts of loss. Tractor stolen from the dealer's lot while being serviced
2--What was tractor used for. Solely or primarily used to service the residence premises. (depending on the state is the difference between solely and primarily)
3--Is it a named peril. Yes theft is a named peril
4--Is there any exclusionary language under the peril. None that fits this loss
5--Was a police report filed. Yes
Do we have coverage for this loss. Yes, based on above.
Then we would move to damages which involves year, make, etc...
I hope that doesn't confuse you. I primarily see two claims for lawn mowers, CUT's and SCUT's. They are fire and theft. There is the occasional vandalism, tree falling on them and some other oddball items, but theft and fire lead all others in my experience. Third party liability claims are an entirely different story. They are lead by object being thrown while mowing etc...