I am making this yule log for christmas which requires pectin NH for the glaze. Can I use any other normal pectin instead of the pectin NH and have the same glossy finish?
No, you can't.
Different pectins set under different conditions. Some require calcium, others require a high percentage of sugar. All have their own optimal pH range.
When a recipe is optimised for one type of pectin, other types won't set properly. Normally, you cannot substitute in any direction.
The linked question from Jolenealaska's comment provides further information.