The "chain" was some sort of rubber zip cord which surprisingly? rotted.
Fortunately I remembered a stash of toilet parts in the basement because I wasn't going to spend any money on this toilet while its replacement patiently waits on the porch.
Success! I poked a hole and attached the chain so the toilet flushes again! and to maybe add some interest to what looks to be a very boring blog post, here is a picture of the inside of the toilet lid.
According to the date, this bathroom remodel was nearing completion 3 weeks after I was born. Though what names start with O? Maybe this is just a response to a question in a pre-texting world in an awkward and/or secret location? If I ever get my rear down to the records office to look up previous owners the mystery may be solved.