I remember this game, and I remember being pretty annoyed at how the cursor didn't change shape on hotspots. I think they eventually issued a patch to fix that though. Can anyone confirm that's the version GOG is selling?

Looks like this is the patch? https://archive.org/details/LITE2PAT

You may want to ask in the release thread: https://www.gog.com/forum/general/release_lighthouse_the_dark_being_89209/page4

Sorry for a bit of necro, but to answer as of October 2018:

This version includes the "Highlight cursor" option in the menu, simply to show points of interaction.
Cursor does not change shape, only brightness.

This highlight feature is flawed, as it will show areas of interaction before you have the necessary item, but still fairly needed to avoid pixel hunts. (A single piece of wire on a table full of clutter, including other pieces of wire for example...)