Hi everyone, I'm coming back to this thread because I found another Indian Head penny at that farm site and I tried some techniques to clean it.
First, here's what it looked like once I gently removed the dirt with water and a "sensory brush" (like a very soft surgical scrub brush).
I was able to see the date (1897) but wanted to see if I could recover more detail.
Front and Back


Notice that there is detail around the outer edge visible.
Next I used warm peroxide, and while it bubbled it didn't really do much to remove the heavy buildup.
So - I tried electrolysis. My thinking was that the penny wasn't worth much and I wanted to see what could be done to remove the buildup on both sides.
I did two rounds of 30 minutes each and then a 3rd round of 45 minutes.
Here's what it looks like now with some oil applied (OO I can't figure out the "lightly brushing" thing, but maybe I need practice):

My thoughts: I think the penny
lost a lot of detail because of the electrolysis. It's most noticeable to me along the outer edges, where I think the fine markings went away. The back seems especially damaged by the electrolysis, because now I can't see much of any detail on the back.
Yes, the electrolysis did remove most of the corrosion (I left a little on purpose, to show what it looked like before), but I think it took copper away with it.
I could argue that the ground here in New Jersey caused the majority of the corrosion, and that would be true - the penny wasn't in great condition when I found it.
But I think my pictures show that electrolysis also took away some of the detail.
I'm going to be hesitant to use electrolysis in the future.