Silver nitrate is somewhat light sensitive in that it will turn gray with prolonged exposure. This is why it is packaged preferably in brown glass bottles. Silver sulfide is not sensitive to light. If it were then sulfide toning of microfilm for archival storage would be valueless.
The Kodak test solution is probably better than the Ilford. The reason for the acidification with acetic acid is to prevent silver oxide from forming with any alkali still present in the paper. In the presence of hydroxyl OH- ions silver hydroxide first forms an then quickly decomposes to silver oxide. Silver oxide is brown or black and its presence would distort the test results.