Fine line tattoos tend to hurt less than traditional tattoos, however some spots definitely still hurt. That being said, I've never had someone get up a leave in the middle of a tattoo. You can do this!
To help illustrate the pain points, I'm going to share a couple of pages out of one of my favorite tattoo books "Tiny Tattoos" by Rebecca Vincent.
In my personal opinion and experience, the most painful spots for my clients have been the fingers, ears and feet. These areas are BONY and you will feel every poke. My least favorite part of my job is inflicting pain on people, and although it's inevitable at times, I have created a system of booking clients with lots of time in between so each client can take their time. I walk people through the pain with breath work and breaks.
If you are in the market for finger tattoos, it's always better to go with fine line tattooing. Fine lines heal beautifully and spread much less than traditional tattoos, and with the skin on the fingers being so thin, a bigger needle can easily go in too deep and cause blowouts and look "smeared" over time. Fine Line Tattoos on your fingers will still need to be touched up yearly since they are constantly in the sun, being washed often and used so much in daily life.