Fixing and Learning About Old Mortise Lock

[Beign]

We have two storm doors from the 1930s or 40s with old storm door hardware. The deadbolt was not working on either set. So, I opened them both and found a lot of dirt in one and a lot of rust in the other. I found a flat piece of metal in both and was not sure what it was for. The deadbolt seemed to work fine with the turn knob without this piece of metal. After searching for awhile, I've learned that it is probably a flat spring. I am not sure what the purpose of this spring is and whether or not I need to find a replacement/ install it. I am including pictures of the one that I opened that was filled with rust. I found a broken piece of metal in there. The picture of the full piece of metal is from the other mortise lock that had been filled with dirt. I would appreciate any help in understanding the purpose of this spring, where it should be located, and whether I need to include it in my repair.

Thank you!