Repyy to u/bluestemgrass at https://old.reddit.com/r/typewriters/comments/1thup7q/reink_ribbon/ RE: Ribbon for a toy Sears Holiday typewriter.
Before you go too deeply here, is the ribbon made of cloth material (nylon, silk, or cotton) or is it a plastic film/carbon type?
If it's the latter, is it a proprietary cartridge or typewriter spools? What width is the ribbon? Cartridges with carbon can be difficult if not impossible to find for these models.
It looks like it may be a Sears rebranded version of some of the Byron Jardine/PETITE toy typewriters. https://typewriterdatabase.com/no_info.525.typewriter-serial-number-database There may be an imprint of the manufacturer on the bottom which would help to identify the original manufacturer.
Most Petite typewriters use T4430 or T4431 ribbon (1/4" wide or 6.50mm) which can sometimes be found on eBay and other sites. It generally requires original spools. These were generally carbon/plastic based ribbon.
If you have the original spools, you might find someone who still manufactures carbon-based ribbon and you can cannibalize it to spool onto your Sears Holiday. Look around for some of the 80s/90s film-based cartridges meant for word processors.
If it did originally have cloth ribbon you might be able to re-ink it, but the process typically tends to be very messy. Generally some glycerine and ink meant for metal stamps (not rubber) will get you where you'd like to go. Some have also soaked their old ribbon in WD-40 as a means of rejuvenation, but this is also time consuming and messy.
More detail/photos of the manufacturing details on the bottom and photos and measurements of the spools and the original type of "ribbon" will help immensely.
If you get the chance, add your example to the typewriter database and include photos of the spools as well as measurements of their width and diameter to help others with these questions/problems in the future.