The instruction to do "one thing at a time" is implied by the Buddha's praise of Sāriputta's practice, which was intense, deep and accomplished methodically one by one:
MN111:1.6: The Buddha said this: “Sāriputta is astute, mendicants. He has great wisdom, widespread wisdom, laughing wisdom, swift wisdom, sharp wisdom, and penetrating wisdom. For a fortnight he practiced discernment of phenomena one by one.
That fortnight was critical for Sariputta because it made him an arahant.
MN111:21.1: And if there’s anyone of whom it may be rightly said that they have attained mastery and perfection in noble ethics, immersion, wisdom, and freedom, it’s Sāriputta. And if there’s anyone of whom it may be rightly said that they’re the Buddha’s true-born child, born from his mouth, born of the teaching, created by the teaching, heir to the teaching, not the heir in material things, it’s Sāriputta.
Multi-tasking entails that one momentarily averts attention from one task in order to attend to other things in rapid succession. Clearly, driving while listening to the radio and thinking about what we want for dinner isn't practicing "one by one". Instead, conventional multi-tasking normally manifests as intermittent aversion to the unpleasant necessities while intermittently attending to the pleasant. The delusion that multi-tasking is effective is what makes it necessary to have laws that forbid dangerous multi-tasking such as texting and driving. Multi-tasking is therefore unskillful.
Practicing one by one is skillful.