By Padraic Halpin DUBLIN (Reuters) - Irish teachers went on strike on Tuesday in a dispute that could close most secondary schools indefinitely, the latest industrial unrest testing the minority government and pressuring the country's still fragile finances. Ireland was spared the kind of walkouts suffered by fellow bailout recipients Greece and Spain during the financial crisis as public sector workers reluctantly stomached deep wage cuts. With doctors also balloting for industrial action and nurses warning of the same, the disputes are putting pressure on a deal the government agreed with most trade unions last year to gradually restore some of the pay cuts by 2018.