SEOUL, Feb 15 (Reuters) - South Korea's presidential candidates formally began campaigning on Tuesday in what is set to be the tightest race in 20 years between its two main parties, dominated by scandals that have allowed a third challenger to potentially play the role of kingmaker.

Polls say voters are looking for a president who can clean up polarised politics and corruption, and tackle the runaway housing prices and deepening inequality that have dogged Asia's fourth-largest economy.

Curbing North Korea's weapons tests and resuming talks would be a plus, but even a record month of missile testing by Pyongyang in January hasn't made foreign policy a key issue for the March 9 vote in South Korea.

But the major issues named in the polls have been overshadowed by scandals and petty controversies, ranging from allegations of abuse of power to spats over one candidate's relationship with a shaman and an anal acupuncturist.

Fourteen candidates have signed up since official registration opened on Sunday, with Lee Jae-myung, the flag-bearer of the ruling Democratic Party, facing off against Yoon Suk-yeol, from the conservative main opposition People Power Party.

Dubbed the "unlikeable election" due to high disapproval ratings and smear campaigns waged by both sides, Lee and Yoon are neck and neck in polls, although Yoon has maintained a slight lead in recent weeks.

A survey released on Sunday by Realmeter showed 41.6% of respondents favoured Yoon and 39.1% picked Lee, while Southern Post put Yoon just 0.5% ahead with 35.5%.

That would contrast with the last three presidential elections, which were largely predictable. The upcoming contest could be the closest since 2002 when an opposition challenger lost to former President Roh Moo-hyun by a 2.33% margin, or 570,980 votes.

"This is the foggiest election we've seen in a while, it's very rare that a likely winner had yet to emerge just three weeks before the vote," said Bae Jong-chan, a political analyst who runs the Insight K think tank.

A former governor of Gyeonggi province, Lee shot to prominence through his aggressive handling of the coronavirus pandemic and his advocacy of universal basic income.

Yoon is a political novice, but has gained popularity thanks to his image as a staunch prosecutor-general who steered high-profile investigations into corruption scandals engulfing aides to former President Park Geun-hye and current President Moon Jae-in.

But growing frustration over mainstream politics and controversy involving both candidates' families have been a fillip for Ahn Cheol-soo, a renowned software mogul and doctor who is a minor opposition contender.