The spectra of Rydberg atoms in the domain of three-level avoided crossings formed by the Rydberg $49{S}_{1/2}$ state and high-$l$ states in the $n=45$ manifold are observed in the standard magneto-optical trap of cesium. We develop a highly accurate method which uses the spectroscopic results in order to refine the quantum defect of the $49{S}_{1/2}$ state from the previous value $4.0495\ifmmode\pm\else\textpm\fi{}0.0001$ extrapolated from $n=6--30\phantom{\rule{0.16em}{0ex}}S$ states [K. H. Weber and C. J. Sansonetti, Phys. Rev. A 35, 4650 (1987)] to the new value $4.049\phantom{\rule{0.16em}{0ex}}78\ifmmode\pm\else\textpm\fi{}0.000\phantom{\rule{0.16em}{0ex}}03$. For this purpose, we determine two characteristic properties of the avoided crossings: (i) the minimum gap between the upper and the lower levels, and (ii) the value of equal gaps between the upper and the middle levels and between the middle and the lower levels. The experimental results for the avoided crossing near 4 V/cm are (i) $(111.7\ifmmode\pm\else\textpm\fi{}1.3)h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, and (ii) $(57.0\ifmmode\pm\else\textpm\fi{}2.1)h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$. For comparison, quantum mechanical simulations based on the published quantum defect yield (i) $109.52h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, and (ii) $56.04h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$. The refined quantum defect is adjusted such that it yields (i) $111.50h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, and (ii) $56.98h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, in even better agreement with the experimental results. The theoretical values of the electric fields for (i) and (ii) differ by 0.03 V/cm, in perfect agreement with the experimental results. The refinement also improves the agreement of their absolute values. The remaining \ensuremath{\sim}1.5% difference is attributed to effects of stray fields.
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