Part of the weirdness on the harp I think is that on the piano, I’m not terribly aware of my right hand. I think this is typical for pianists, in that our right hands tend to do mostly close-quarters detail work and our left hands tend to do long jumps, octaves, and generally things that require more mobility over the keyboard in longer spans. That tends to require more visual oversight. I don’t think it’s an issue of handedness either; I’m left-handed, and one would think that I could trust my left hand more, but the job it does is simply more spread out over the keyboard. Octave leaps in the right hand are unusual and need to be practiced, but octave leaps in the left are simply par for the course. Rapid close work in the right hand, where fingering is a big consideration, is also par for the course, but when that shows up in the left, one needs to pay it special mind.
I’m looking forward to getting to that point on the harp, and as I go, I’m trying to make myself not watch my right hand, so that I get used to just noodling and knowing where the strings are. That will enable my left hand to improve in that my attention won’t be split between them.