I've had time to do a bit of research on the Elgin. Based on online pictures and scans from Sears & Roebuck catalogs, I might have a 1939 Twin 20, or the most basic model. I believe the paint might be original, which if this is the case, is in amazing condition.

The center bike best matches my Elgin. The distinctions include the cutouts in the chainring, the lack of a rack, and any other frame embellishments.



Mine appears to be missing the front fender head light, and the head tube enclosure. I plan to ask the family if they've come across these items in preparing the house for sale. Here's a closeup of what I hope to find. There is an ebay seller who is making repops of the head tube enclosure at $130 each, so a search of their basement might prove productive.



A close up of mine missing the enclosure.