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FDM printer?
If you want to print one, maybe you should outsource it (let it print the tag on both sides), even the most affordable printers are in the \$100 - \$150 price range. If you want a printer and use it also to create ID tags, you could go for an FDM printer. Considering your request of having the tag inside (and through) the ID-card you need a dual filament option (one or two nozzle arrangement). If the tag can sit on top you can print it with a filament change with a single filament single nozzle printer. But, don't expect to get crystal clear prints (see experience printing signs below)!
Alternatives
As an alternative, you could print a blank PLA ID-card and laser mark the tag onto both sides, see e.g. this video.
If it is a small batch you can also consider printing/lasering stickers and stick these onto blank ID cards.
From experience
I've done some signs with black letters on a white background for "on-lay", inlay and through arrangements using a more expensive (for home use) dual extruder 3D printer (Ultimaker 3 Extended about \$5000,-) with PETG, but the results were not very satisfying. Usually the black smears out on or in the white no matter tweaking the options. Considering the size of an ID-card, the amount of tag squares, this is even more likely to happen when you print at that small size (the signs I printed were sized similar to the "A5" paper standard).
From my experience I would say that a 3D printer may not be the best solution for your task.
There are two ways to print a card to a Windows printer instead of the standard printer.
•Click on the Name of the printer in the Windows printers tab in Explorer Menu or
•Select the Printer Name from the drop down menu in the Windows printers section of the Print Tab.
In both cases, the Print command window appears.
In the Selected printer group you can find the information of the printer you are printing too like the Name of the printer, the Status of the printer, Type, etc.
Just like in normal Microsoft Office Applications, in the Print range group you can set to print the Selected record, All records, or a selection of Records. The Number of selected records is indicated in this named field.
Next to the name, the button Properties... gives access to the printer-properties window, allowing to adjust any settings before starting to print. Generally, it is not necessary to change the printer properties once they have been defined for the first time.
In the Copies group you can enter or select the amount of copies that needs to be printed. By default CardExchange® Producer prints one copy.
If the card uses a global counter, in the Global counter group you can see the number indicating the global counter number that will be used for the first card to be printed. For each consecutive card the global counter will be incremented by one. The global counter can be edited to change this number to another value. It is up to the user to decide whether changing the default value is necessary.