Second home mortgage vs. investment property mortgage?

We are considering buying a second (vacation) home. A cabin in the mountains, about 150 miles from where we live. It's much cheaper to get a second home mortgage than an investment property mortgage, but we would ideally like to get some rental income from the property as well. It probably wouldn't be a... show more We are considering buying a second (vacation) home. A cabin in the mountains, about 150 miles from where we live. It's much cheaper to get a second home mortgage than an investment property mortgage, but we would ideally like to get some rental income from the property as well. It probably wouldn't be a lot, definitely not enough to pay the mortgage. I've gotten a lot of hemming and hawing from the mortgage specialists I've spoken with about whether we'd qualify for a second home mortgage. Is there a specific line lenders use to separate a second home from an investment property? Any rental income at all? Or is there a threshold amount, or a threshold number of days, or percentage of owner occupancy? We're going to be 100% honest with the lender, but we'd like to know in advance if we need to commit ourselves to a certain limitation on rental use.

Thanks!
Update: I appreciate the answers, but they don't quite get to the heart of my question, so let me rephrase it. The home would primarily be for our personal vacation use. But - since we care about not committing mortgage fraud and want to be sure we're on the right side of the law - we need to know if ANY... show more I appreciate the answers, but they don't quite get to the heart of my question, so let me rephrase it.

The home would primarily be for our personal vacation use. But - since we care about not committing mortgage fraud and want to be sure we're on the right side of the law - we need to know if ANY amount of rental income is too much for that type of loan.

What we have in mind is letting people rent it on weekends we're not using it. It would never be occupied by a tenant for more than a few days at a time. No long-term lease. It's in a ski area and I imagine we could find renters for some of the weekends we don't use it during the winter months.

We would probably stay there several whole weeks during the year, and numerous more weekends, and would probably be the ones to occupy the cabin more than 50% of the time it's occupied.

Would that situation qualify for a second home mortgage? Or would any rental income at all mean we'd need an investment mortgage?
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