The Talmudic source for waiting between meat and milk: Mar Ukva testifies that his father would wait from one meal to the next, while he himself waits the full duration from one meal to the next — the Talmud's basis for the waiting period.
אָמַר מָר עוּקְבָא: אֲנָא, לְהָא מִלְּתָא, חַלָּא בַּר חַמְרָא לְגַבֵּי אַבָּא, דְּאִילּוּ אַבָּא כִּי הֲוָה אָכֵיל בִּשְׂרָא הָאִידָּנָא, לָא הֲוָה אָכֵל גְּבִינָה עַד לִמְחַר עַד הַשְׁתָּא, וְאִילּוּ אֲנָא – בְּהָא סְעוֹדְתָּא הוּא דְּלָא אָכֵילְנָא, לִסְעוֹדְתָּא אַחְרִיתָא – אָכֵילְנָא.
Mar Ukva said: I am, with regard to this matter, like vinegar, son of wine, with respect to Father, i.e., my practice is inferior to that of my father. As Father, if he were to eat meat at this time, would not eat cheese until tomorrow at this time. But as for me, only at this meal, during which I ate meat, do I not eat cheese; at a different meal on the same day I will eat cheese.