You cannot use the sun's rise/set tables to correct your clock when moving a lot, they are also affected by the weather, changing the atmospheric refraction. But I believe any modern electronic watch is precise enough within a 6 month period of time (one could measure the drift precisely enough beforehand to correct for that anyway, if absolutely necessary, but sextant's measurements might be not precise enough to be affected by the modern watch pace drift fluctuations). Then, every 6 month you could observe the Sun around equinox in order to figure if your clock's correction must be adjusted.