You can get tattoos that are you skin tone, but they aren't invisible, they will show up if you get flush or tan.
There also are UV tattoos that onto show up under blacklight. How visible they are varies, but there is usually a ghosting with them.
Both cases, the ink fades faster than other colors. How fast that happens depends on the person and how much sun exposure you get. You can get touch ups every 2 years to keep the UV bright, but it does muddy the tattoo the more you do that.