Yes I would like to fix the old one, but I wouldn't know where to buy the parts from. If you know, maybe you could tell a younger (37) guy where to but them from. I like the way they look and it would be cool to keep them if possible.
Looking at the picture of the loser. It appears that it really needs just two parts to work. Everything it needs are still current production. The snap-in receptacle and the turn-on-off switch might be available at a big box (LowDepot etc). The receptacle will be in wiring parts and the switch as well as the nut for and a shade will be with lamp parts. Also in lamp parts, you may find the long screws to remount that fixture.
If you do not find the parts there, then disconnect (label the wires) and take the fixture to a really truly lamp store. There are also lamp parts suppliers on the web, but if you are unclear on what you need, that may be a bad idea.
If you are slick, you could get the switch for the AC side that makes it a three way so you don't have to light both bulbs.
You can also save a lot of future damage by using CFL (curly fried light) bulbs. These produce much less heat.
Since it would be doubtful that you will be able to find any NOS or reproductions of your dual voltage fixture you may need to get creative in repairing it.
For the most part you may be able to find “off the shelf” parts which may fit or be “adapted” with modifications to the fixture.
However please understand that many of these parts may not be available at your local Home Depot, Lowes or many electrical supply house since they are no longer “common usage” and more of a specialty item and tend to be “slow moving” inventory.
In my area, both Home Depot and Lowes have slashed a lot of “slow moving” inventory from their shelves, simple items like toggle, push button switches are of such low demand that they are not easy to find in store anymore. Many items which used to commonly used in homes and such have been obsoleted or gone out of style.
If inventory does not turn fast enough they no longer reorder it to stock the shelves, period.
In other words most likely you will most likely need to order online or mail order.
If you want to keep the vintage period correct rotary switches then take a look at the ones I found. Although since the contacts are outside the electrical box, I myself would use a toggle or push button which would be safer in the event the switch is ever broken again (push button and toggles will not expose the live contacts outside the electrical box in the event of breakage).
The only thing I have not found is the vintage Bakelite 12V lamp sockets but you might be able to substitute a newer bayonet style 12V bulb socket which would not have the Bakelite cover if you need to.