Should my second business be separate or a division of my current S Corp?
My first question would be is there a market for this business? Is it something that your customers typically buy with your current products or services or is it something they are asking if you offer?
Starting out, I would say to "test and measure" the idea with your current customer base to make sure it is a service or a product they really want to buy.
Then, add it as an additional service or as part of a "package" of services you offer and this package may be at a price point slightly higher than you are currently charging.
Test first before committing resources and marketing dollars and efforts to generating more leads to a new business.
You have the advantage right now (at least it sounds like it) of a "captured" base of current customers. Go back to them first. You already have a relationship with them and a reputation for your work.
Grow your "start-up" from this base, and you'll have a better idea of your new idea is a winner, and deserving of its own unique company.