Achieving a syrup-like consistency necessitates something like a sugar. If you boil sugar and water together (simple syrup), you get that consistency. If you boiled it without the sugar, you'd end up with an empty pot after the water had boiled off, but would never see a change in the consistency beyond the water evaporating into steam.
It's unclear what you mean when you say you're trying to use this "syrup" to absorb other flavors. Certainly you can use a milder, "unflavored" syrup such as simple or agave in a savory preparation, as long as you tone down the inherent sweetness with fat, salt, or acid, but the use of a syrup is largely textural, and it doesn't seem to me that a "syrup" is really what you're looking for. A syrup is, in itself, a flavor component in addition to all its other qualities that I and others have mentioned.