Your last sentence seems a bit judgemental and insulting since they specifically noted they were asking about giving a compliment when NOT trying to meet women (hit on them). But perhaps im mistaken why you included that(which will be just confusion on my end then)

Your points put into words things ive done but never really realized it or would have been able to explain.

I say this because i have complimented tattoos on more than a few occasions and i have rarely noticed an uncomfortable reaction (i judge this by the fact that they talk about the tatoo ive mentioned for longer than i spoke words).

I am fascinated by what people choose to permanently put on their body. There are often very meaningful reasons for it, but not as rarely as i would have thought it is a very quick spur of the monent decision. Most of the time this happens at a check out/til in a store.

I will typically just make a comment about the work itself, not about the placement(unless its on a spot ive been told is very painful as many people have such different experiences, "ive been told that is a tender spot for a tattoo" or some such. But its an honest question because i have been told that)

Common things that prompt me to comment are striking/vibrant colours, im curious how old the tattoo is as some colours are prone to fading badly Or very clean and clear lines, especially when they are delicate or just very thin.

I have a specific reason or curiosity which prompts me or i dont say something which i think is why i seem to be able to successfully give compliments/comments to strangers in public. But ill also compliment guys in public as well for the same reasons/circumstances and im definately not attempting to hit on or pick up guys(ide be flattered if a guy thought i was hitting on him though)