I believe you are correct that this is the Lucky Starr series by Isaac Asimov (writing as Paul French).
Points that match:
Does anyone remember which novel features an interactive tattoo display on forearm?
Check. David 'Lucky' Starr is a member of the Council of Scientists. They have a tattoo embedded on the inner side of their right wrist/forearm as a means of identification. They activate it as follows:
I've seen you in video reels often enough. But why don't your wrists show the mark? I've heard all the members of the Council were marked.\" \"Where did you hear this? And who told you the library at Canal and Phobos is the Council of Science?\" Bigman flushed. \"Don't look down at the farmboy, mister. I've lived in the city. I've even had schooling.\"\"My apologies. I didn't mean it that way. Will you still help me?" / Not until I understand about your wrists.\" "That's not hard. It's a colorless tattoo that will turn dark in air, but only if I want it to.\" \"How's that?\" \"It's a matter of emotion. Each human emotion is accompanied by a particular hormone pattern in the blood. One and only one such pattern activates the tattoo. I happen to know the emotion that fits.\" David did nothing visibly, but slowly a patch on the inner surface of his right wrist appeared and darkened. The golden dots of the Big Dipper and Orion glowed momentarily and then the whole faded rapidly.
I am trying to find the book where this technology is featured. It could have either been one of Asimov's "Foundation" books, or Lucky Starr series.
Check. This is the Lucky Starr series.
It may also be that my memory is betraying me and it was written by someone else entirely, although it was definitely in existence by 1985-ish, which is the timeframe when I was reading this. (Probably written in the 1940's - 1970's)
Check. Written in the 1950s. I read this myself back in the 70s and enjoyed it very much. A bit dated. But, good juvenile science fiction.
I believe one instance is where the character arrives at a particular planet, he's looking for someone, and in a remote area where no one can see him, he pulls up his forearm and the tattoo "activates" and then he does some type of interactive search or other task.
Check. See above.
I think I remember it's normally not visible, but when he pulls up the forearm and taps it with a finger from the other hand, it lights up. Also there might have been a reference to some "long lasting" (nuclear?) power source for some of the other devices that this individual used.
Check. See above.
Update this character is some type of enforcer in the story (investigator, PsychoHistory agent, etc. which is why he's looking for someone upon landing on the planet)
Check. Lucky Starr became an agent for the Council of Scientists. Again per Wikipedia: "In a later novel in the series, Lucky Starr and the Oceans of Venus, the Council of Science is described this way: "In these days, when science really permeated all human society and culture, scientists could no longer restrict themselves to their laboratories. It was for that reason that the Council of Science had been born. Originally it was intended only as an advisory body to help the government on matters of galactic importance, where only trained scientists could have sufficient information to make intelligent decisions. More and more it had become a crime-fighting agency, a counterespionage system. Into its own hands it was drawing more and more of the threads of government."