There are cartridge holders out there that you can buy for pennies but if you need one and don't have one on hand this might help you out.
Obviously, if you tattoo people these should not be ever reused and I guess they should be sterilized before use.
If you do like it and it doesn't fit your needles feel free to send me a message with pic and I will edit it to suit your needs when I have a minute.
Btw these are the ballpoint tattoo cartridges I use they are quite good at learning the right pressure as too little and you don't draw anything and too much and you ruin the paper.
https://s.click.aliexpress.com/e/_okqJeQ0
The author marked this model as their own original creation.