Yes, manually making the EOS contact/break contact should make a sound or show something on display while in switch edge test. If left & lower right are testing good, then it stands to reason problem lies on upper right's adjustments (especially if this was the one you were just working on). That being said, if all are within limits, perhaps something else power related is going on.

To answer your question "What would be wrong about the EOS that would cause a fuse to blow?". My simple-minded (me, not you) explanation would be that normally no power is going through except for minimal instances (pushing button), but if the leafs are touching when they shouldn't be (or vice versa) all the time, it's getting juiced more than was intended & blowing the fuse is a precautionary measure to avoid frying further components. Good luck.

I see it's been mentioned that perhaps something is grounding out, I'd double check that and also ensure wires were soldered to correct terminals on the coil.