We continued our ground-based observing project with the season-long observations of ZZ Ceti stars at the Konkoly Observatory. Our present targets are the newly discovered PM J22299+3024 and the already known LP 119-10 variables. LP 119-10 was also observed by the TESS space telescope in 120-second cadence mode. Our main aims are to characterise the pulsation properties of the targets and extract pulsation modes from the data for asteroseismic investigations. We performed a standard Fourier analysis of the daily, weekly, and entire data sets, together with test data of different combinations of weekly observations. We then performed asteroseismic fits utilising the observed and the calculated pulsation periods. For the calculations of model grids necessary for the fits, we applied the 2018 version of the White Dwarf Evolution Code. We derived six possible pulsation modes for PM J22299+3024 and five plus two TESS pulsation frequencies for LP 119-10. We note that further pulsation frequencies may be present in the data sets, but we found their detection ambiguous, so we omitted them from the final frequency list. Our asteroseismic fits of PM J22299+3024 give 11400K and 0.46M_{sun} for the effective temperature and the stellar mass, respectively. The temperature is ~800K higher, while the mass of the model star is exactly the same as was earlier derived by spectroscopy. Our model fits of LP 119-10 put the effective temperature in the range of 11800-11900K, which is again higher than the spectroscopic 11290K value. Moreover, our best model solutions give M*=0.70M{sun} mass for this target, which is near to the spectroscopic value of 0.65M{sun}_ and likewise in the case of PM J22299+3024. The seismic distances of our best-fit model stars agree with the Gaia astrometric distances of PM J22299+3024 and LP 119-10 within the errors, validating our model results.