First,
It’s under the steering column
I don't think so. The P1000 does not have a parking break to my knowledge, and I own one.
Just as a comment: My P1000 does not have any tendency to move at all on my trailer with the transmission in lock mode. Some, if not most, straps tend to stretch (cheaper straps stretch more). I would highly recommend that the straps be checked after trailing for 5 or 10 miles. Of course, tighten if required, and repeat this check until they remain taught. This is one of the most important safety practices in my mind. If you don't have snaps to keep your S hooks from falling off, then that is another risk.
Good straps are not cheap, but they don't stretch nearly as much. Get the snap locks on the S hooks for sure. Info is available on-line regarding the quality of straps. I went through 3 sets of straps before I figured out that I should buy high quality straps. LOL
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