To close the loop here, I was able to solder in the new power cord. Before reinstalling everything, I took my Dremel tool with a wire brush and removed the various rust spots, just about all of it was surface rust. I then applied a light coat of WD40 to give it a bit of luster. I love the stamped "THE LIONEL CORPORATION NEW YORK, N.Y." on the bottom. The top of the transformer has "MADE IN U.S. OF AMERICA".
The Lionel 1010 Transformer was made in the 1961 to 1966 period and was included with the lowest of the low-end sets. But here we are some 60 years later, the transformer just needed a new cord (part # B-292 block L 6’ power cord repro) which are just $2.85 from the Train Tender if you buy 10. These transformers are considered "cheap" by many, but the craftmanship of these units is amazing, and have stood the test of time. And my thanks to my friends on the OGR Forum for providing some helpful hints.