John Duran is courted by former rivals Bobby Shriver, Sheila Kuehl

A day after L.A. County Board of Supervisors candidate John Duran finished third in the June 3 primary, first-place finisher Sheila Kuehl sent him a dozen white roses. A few days later, Bobby Shriver, who finished second, took him out for drinks.

As Kuehl and Shriver head to what is expected to be a tough and expensive November runoff, each is trying to win Duran’s endorsement. The little-known West Hollywood city councilman got a surprising 16% of the vote ahead of five other candidates.

But while he has been willing to meet with the two finalists, he hasn’t said who he might support, or if he will endorse at all.

“I told them I’m not likely to do anything between now and the end of summer,’’ Duran said. “I want to see how the campaigns unfold.... They are both a little more liberal than I am. So I’m still concerned about who’s going to hold the solid center in the county.”

Political analyst Raphael Sonenshein said Duran’s endorsement in the race to succeed termed-out Supervisor Zev Yaroslavsky could be helpful, especially in attracting more conservative voters in the northeast San Fernando Valley, where he performed well.

But if an endorsement is in the cards, it had better come fairly soon. The “shelf life” of Duran’s backing, Sonenshein said, could diminish in time. “He’s not an established brand yet,’’ Sonenshein said. “Voters’ attention drifts and an endorsement is much more likely to get washed out if you wait too long.”

Duran, 54, was considered a long-shot in the field of eight candidates even though he spent 14 years on the West Hollywood council. But after impressing audiences at debates, where he positioned himself as a more fiscally conservative choice among the major Democrats running for the seat, he began picking up support.

In the days before the election, he received a number of influential endorsements, including from Supervisor Gloria Molina, Mayor Eric Garcetti and the Los Angeles Times. In unofficial primary results, he finished a distant third behind the 36% polled by Kuehl and 29% for Shriver.

Shriver, who has been backed by several business groups as well as some unions, said it would be a “big deal” for his campaign to win Duran’s endorsement. The former Santa Monica council member and mayor said he and Duran share a background in local government and they both advocate for diversion of mentally ill jail inmates into treatment centers.

Shriver said he and Duran became friendly during their months on the campaign trail. “We like each other, I think,’’ he said.”He has a great sense of humor, which I think is an underrated quality.”

Kuehl, meanwhile, notes that she and Duran, who are both gay, have long advocated for social justice in the LGBT community. “Every candidate wants the endorsement of those who ran against her,” she said. “I’d love to have his.”

In 2012, Duran had a well-publicized political feud with Torie Osborn, Kuehl’s longtime friend and advisor, who was then running for a seat in the state Assembly. Duran backed Osborn’s rival, Betsy Butler, and became incensed by what he saw as Osborn’s camp stacking a meeting of West Hollywood Democrats to win an endorsement.

In a You Tube video of the meeting, Duran is seen condemning Osborn after the vote, pointing his finger and vowing “West Hollywood will not forget!”

Both Duran and Osborn said they have since buried the hatchet. “Torie and I had a private discussion a couple of months ago where we cleared the air between us,” Duran said. “It won’t be a factor in my decision.”

More important, he said, is following his own instincts while representing constituencies that were key to his third-place finish.

“I’m getting calls from both LBGT activists who want me to endorse Sheila because she’s gay and from the business community who say I should support Bobby because he’s more pro-business,’’ he said. “I’ve got a tough decision ahead.”

catherine.saillant@latimes.com

Follow me at @csaillant2