As often happens in English, you can get some insight into the shades of meaning of each word by looking at their etymologies.
Reveal comes from Latin roots meaning "to pull back a veil". It suggests that the thing revealed was hidden behind something, perhaps deliberately, perhaps not. A "revealing dress" is a dress that exposes a lot of skin. Here's a book titled The Great Pyramid Reveals Its Secrets. Another book: What the IRS Doesn't Want You to Know: A CPA Reveals the Tricks of the Trade.* If the aspects of personality that you can deduce from a person's sleeping position are of a kind that most people prefer to keep secret, then reveal is probably the better choice.
Indicate comes from the same Latin root as index, as in "index finger". It means to point to something, to establish a fact or conclusion in a plain way. The needle on a speedometer indicates the car's speed. An economic indicator is a statistic that provides information about some aspect of a nation's economy. A chemical indicator indicates some attribute of a solution, like its pH, by the color it turns to when exposed to the solution. As these examples suggest, "indicate" would give the sentence an objective, precise, scientific sound. If a person's sleeping position "points to" the personality traits you're describing much like the way a speedometer's reading "points to" the car's speed, then indicate is probably the better choice.
The better choice depends on what you want to emphasize—the way you'd like the reader to think of the relation between sleeping position and personality.
See also the entries for "reveal" and "indicate" in Merriam-Webster's Dictionary of Synonyms. There you'll find more synonyms and more subtle distinctions and connotations spelled out—or perhaps I should say, revealed, if I want to make it sound like those synonyms have long been hidden from public view but now are finally available for anyone to see.
* IRS = Internal Revenue Service, the part of the United States government that collects federal taxes. CPA = Certified Public Accountant. So, the book is about ways to avoid paying taxes, which most people don't know about.