You're not getting a second mortgage because at the moment you don't have a mortgage, correct?
You're getting a mortgage on your house for the second time, correct?
If that's the case, we've been there. We paid off primary residence in 2008. In 2014, we found a second home/weekly summer rental/future FIRE home. We found it much easier to get a mortgage on our primary residence (which had been mortgage free for six years) and paying cash for second home. Not only is it much cleaner from a tax standpoint -- all mortgage interest from primary is tax deductible -- it's much more difficult to get a mortgage on a second home (even if you don't have one on your first.)
As a self-employed person, I learned that I was not going to get a mortgage on a second home regardless of my lack of existing mortgage and regardless of my balance sheet. They want to see that W-2 income. Ridiculous.