Since it was pretty obvious what the problem was, the only catch was to find a part that would work in a 45-year-old oven. A call to the manufacturer yielded nothing for a model of this vintage. After a brief chat online, Heidi T. took my model number and promised to follow up with the appropriate part number. Within a couple of hours, I received an e-mail with the part number.
Once I received the replacement heating element, the repair was trivial.