A search for a very light Higgs boson decaying into a pair of $\tau$ leptons is presented within the framework of the next-to-minimal supersymmetric standard model. This search is based on a data set corresponding to an integrated luminosity of 19.7 fb$^{-1}$ of proton-proton collisions collected by the CMS experiment at a centre-of-mass energy of 8 TeV. The signal is defined by the production of either of the two lightest scalars, $\mathrm{ h_1 }$ or $\mathrm{ h_2 }$, via gluon-gluon fusion and subsequent decay into a pair of the lightest Higgs bosons, $\mathrm{ a_1 }$ or $\mathrm{ h_1 }$. The $\mathrm{ h_1 }$ or $\mathrm{ h_2 }$ boson is identified with the observed state at a mass of 125 GeV. The analysis searches for decays of the $\mathrm{ a_1 }\ (\mathrm{ h_1 })$ states into pairs of $\tau$ leptons and covers a mass range for the $\mathrm{ a_1 }\ (\mathrm{ h_1 })$ boson of 4 to 8 GeV. The search reveals no significant excess in data above standard model background expectations, and an upper limit is set on the signal production cross section times branching fraction as a function of the $\mathrm{ a_1 }\ (\mathrm{ h_1 })$ boson mass. The 95% confidence level limit ranges from 4.5 pb at $m_{\mathrm{ a_1 }}\ (m_{\mathrm{ h_1 }})=$ 8 GeV to 10.3 pb at $m_{\mathrm{ a_1 }}\ (m_{\mathrm{ h_1 }}) =$ 5 GeV.

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