Get the Death Certificate!
Ok, here goes. I'm going to tell you what solves a majority of the genealogy cases I work. Death certificates. Seems simple, right? In concept, I think it is. In practice, not so much.
First, trying to understand the ordering process and know what information to fill in on the application is not always easy. Each state's website is different, different forms (that sometimes don't make sense), different ordering processes, etc. Sometimes, it's just too confusing.
And intimidating. What if you order the wrong one? What if I maybe don't know enough to even order it? How many of those blanks can be, well, blank?
In both of the above, I say "try." Don't hold yourself to perfection, just give it a try. Decide up front that you're going to try it out just so you'll learn how to do it. That the learning experience is the goal. Call the office that oversees fulfillment. Humbly ask for advice. Ask them to educate you about the rules and what must be included on the application.
Then order it! And order certificates for other family members that may unlock secrets about your target ancestor. For example, order certificates for their siblings, nieces/nephews, cousins, etc. If your ancestor's certificate did not reveal what you hoped, maybe another family member's will.
After you receive the certificate, really study it and mine the data. Inspect every tiny detail for clues. Is the spouse listed? Who was the informant? What hospital were they in? What funeral home? Cemetery? Do any of those places still have records?
Don't be intimidated. Get the certificate. You'll be surprised how much you learn from it.