My reasoning about pilots on the stove top is that they could easily "blow out", especially if the stove is near a door like ours is. Then, since stove top pilots don't use a temp probe shutoff, you WOULD have propane coming into the trailer, which is a pretty small, confined space.
The oven is more protected, so I doubt blowout is as much of a problem.
I wonder if you could see under the stove top with a small mirror to confirm the presence or absence of a pilot light?
I can't recall anyone else in this forum talking about pilot lights for the cooktop.
- Jack