Tuesday, June 2th 1998, 2:04AM

IN MOST of the television news coverage in the hours and days after Phil Hartman was shot dead Thursday by his wife, Brynn, who then killed herself, viewers saw Hartman paired in vintage "Saturday Night Live" footage with fellow ex-cast member Jan Hooks the two of them as Bill and Hillary Clinton, Ron and Nancy Reagan, and even Jim and Tammy Faye Bakker.

Watching that coverage, Hooks saw the same thing and every clip reminded her of what a fine talent and good man Hartman was, and what fond memories she had of him, and how she owed it to him to share some of those memories.

"I want to do something for him," she said at the end of a long, deeply personal, sometimes tearful phone conversation late Sunday afternoon. "And to tell the world what a wonderful person he was, maybe that's what I can do."

Hooks met Hartman, briefly, on the set of the 1985 film "Pee-wee's Big Adventure" but really bonded with him a year later when they, along with Dana Carvey, Victoria Jackson, Kevin Nealon and A. Whitney Brown, joined the 1986 class of "SNL."

"I remember being absolutely awestruck by Phil's audition," Hooks said, recalling that part of his routine was a bit in which Jack Nicholson was speaking German. "He was this whirlwind of amazing talent."

Hartman told her once that Jesus was among his very favorite characters to play; she also treasures his Barbara Bush, which was a lot more than a shot at man-in-drag cheap laughs.

"They [the show's costumers] gave him the look, the dress, the wig," Hooks said, "but he played her with such dignity, such integrity, and played her so straight, she was always a lady."

At rehearsals, Hooks said, Hartman was "the only one who carried around a script and studied it."

On the air, she noted, his discipline carried over to his performances, which always were based in reality.

"Phil knew how to listen," she said. "And he knew how to look you in the eye, and he knew the power of being able to lay back and let somebody else be funny, and then do the reactions. I think Phil was more of an actor than a comedian."

Also, Hooks added, "Phil never had an ounce of competition. He was a team player. It was a privilege for him, I believe, to play support and do it very well. He was never insulted, no matter how small the role may have been."

Hooks, who admits to severe stage fright, remembers fondly some of the times Hartman managed to loosen her up despite the pressures of live television: when his Frank Sinatra made a pass at her Nancy Reagan, or when he played a drunken Ted Kennedy to her Kitty Dukakis ("That was a moment of just uncontrolled, absolute craziness").

She retains an equal fondness, though, for the more serious times.

'PHIL was my rock," she said wistfully. "He was so solid. Just absolutely serene.

"During the [1991] Gulf War, 'SNL' had become this wonderful favorite place for crazy people to call in bomb threats." On one such night, Hooks said, she panicked and refused to go on.

"Phil and I were in that show's first sketch. He was the Anal-Retentive Chef, and I played his mother. I'm telling you, I was terrified . . .

"But Phil looked at me, and he always had a way of just wordlessly calming me. He I'm going to start crying he put his hand out, and I grabbed on, and it felt like an oak tree. It was the most grounding, calming, serene feeling, that he helped me get through that."

Hartman and Hooks, with their similarly realistic performing styles, were paired on "SNL" so often from 1986 until Hooks' departure in 1991 (Hartman left three years later) that even Hartman's wife noticed.

"Brynn joked about the fact," Hooks remembered, "and said, 'You know, I think you and Phil are married on some other level.' We would laugh about it in some make-believe world, Phil and I were always a couple."

And to Hooks, the Hartmans, in real life, seemed a very happy couple.

"Phil, while he was a wonderful listener, didn't offer a lot," Hooks said. "He was pretty tight-lipped about his own problems, if he were having some. I can't honestly say that he shared a lot with me about his home life.

"But Brynn was always very sweet to me, and she would come to the shows, and bring the children into rehearsal. To me, it just seemed like a lovely, happy family."

Asked about the rumors that Hartman's wife may have had a problem with cocaine addiction, Hooks answered carefully but candidly.

"Brynn did briefly, years and years and years ago, talk about her past problem with cocaine," she said. "But it was almost like a war story, at that point it was so much in the past for her.

"It's only now that I've heard, since this horrible event, that she was messing around with it again. And to hear her, 10 years ago, talk about it, it was like hearing her say, 'Oh, boy, I'm glad I survived that.' "

THE LAST TIME Hooks visited the Hartmans at their Encino home was last Halloween: "Phil was smoking a cigar out in his yard, and we were just talking about life and the business, and he was just easy to be with, and they seemed fine."

More recently, Hooks saw her former "SNL" colleague a little more than a month ago, when they both guest-starred on the season finale of NBC's "3rd Rock From the Sun." She played Vicki Dubchek; he, in an equally gregarious and funny role, played her jealous ex-boyfriend, Randy.

"I had no idea he was going to be playing my boyfriend," Hooks said, "and they [the producers] made it a point not to tell me. They wanted it to be a surprise that it was Phil. So they flew me out, and I didn't know until I walked into the read-through room, and he was sitting there, and it was this wonderful, pleasant surprise.

"It was the last time I saw him."

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