My home, built in the late 1950s, has these cute little additional locks on top of the main doorknobs to many of the interior rooms. I can't seem to find the correct term for these locks, which would allow me to find parts for them, etc., as several are broken. Photo attached. Any ideas?
You can try a different search phrase as "Thumb Turn Security Latch".
There is a seller on eBay that has new stock available in range of finishes. Here is a picture of the offering.
Considering the price you may just want to consider purchasing new units instead of trying to locate parts for the old ones that are broken.
The trade name for these seems to be: Deltana mortise bolt
You can find those at many web sites including at MyKnobs.com.
Here are some dimensional pictures from a Deltana specification sheet so you can compare to your existing items.