My tomato sauce is very watery
It has flavor, but its consistency is too thin. Will letting sit over medium low heat evaporate enough to increase its density or is this useless? Would bringing it to a boil help more. I don't want to ruin its flavor and am afraid bringing it to a boil with high heat will do just that.
Yes, cooking it more to evaporate off some of the liquid will definitely help. This is called reducing a sauce. A moderate simmer would be the appropriate temperature. You want to see occasional bubbles but definitely not a rolling boil. Stir it occasionally, making sure to get the bottom of the pot to avoid any scorching. It is possible to have it be quite liquid on top and rather dense in pockets on the bottom, which can then get well above 212 F and reaching the point of burning.
Why a simmer instead of a rolling boil?
You can boil pretty quick for about the first 1/3 to 1/2 volume. Beyond that, the stuff likes to burn to the bottom of the pot. Turn down the heat. Do it gradually, and keep checking the bottom. With practice, an unburnt puree is not difficult. I've never gone on to the level of paste from there. Investment in tomatoes and time is far too high.