A weak magnetic field times tunnelling by rotating spin. What is the hand?

Answer: Spin precession angle

Spin precession angle ✓ — Correct. The spin precession angle is the clock hand: in a magnetic field, spin rotates at a known rate, so rotation can mark time spent in a region. The catch is quantum interference; the final spin can combine many duration amplitudes, so it may not reduce to one ordinary rotation angle.

Local heat deposit — Local heat would be a crude marker, not a weak clock. If the timing device leaves enough heat to read easily, it has probably disturbed the tunnelling event and damaged the interference. The Larmor idea is subtler: mark the passage with spin while perturbing the barrier as little as possible.

Arrival flash timing — Arrival flashes can time ordinary flight after the particle has left the barrier, but they do not directly say how long it spent inside. That distinction matters because delay after exit and duration in the forbidden region can diverge in quantum mechanics. The Larmor clock tries to couple to the region itself.