Turn-taking is ubiquitous in conversation and is the normal case against which alternatives, such as interruptions, are treated as violations that warrant repair.
Furthermore, turn-taking involves highly coordinated timing, including a cyclic rise and fall in the probability of initiating speech during brief silences, and involves the notable rarity, especially in two-party conversations, of two speakers’ breaking a silence at once.
These phenomena, reported by conversation analysts, have been neglected by cognitive psychologists, and to date there has been no adequate cognitive explanation.

Source : Psychonomic Bulletin and Review, 12 (6), 957-968

In 2005, the paper cited above offered a possible solution : that the two people conversing might have in-built mental 'oscillators' which synchronize on the syllable rate. Thus allowing turn-taking, and interruptions with precise timing.

Here, we propose that, during conversation, endogenous oscillators in the brains of the speaker and the listeners become mutually entrained, on the basis of the speaker’s rate of syllable production.

[source as above]

To date, the precise mechanisms of any 'endogenous oscillators' are not known.

If there is such a system operating, then it would presumably depend on a precisely-timed mental clock mechanism of some kind. Short and long term timing mechanisms do appear to exist, but their details are also unknown. See : Rhythm perceptionplugin-autotooltip__plain plugin-autotooltip_bigRhythm perception

Humans (and some other animals*) have an innate sense of 'rhythm', i.e. the ability to detect and react with 'beats' in musical compositions. Professional drummers and percussionists can 'beat time' with accuracies of just a few milliseconds per beat (ref.