 Finite pulse count for a falling Schwarzschild beacon

A freely falling source emits optical pulses at proper times $\delta +nP$, for integers $n\ge 0$. If its horizon-crossing proper time is finite, only pulses beginning before $s_H$ can escape. Their number is the displayed ceiling, for $0\le \delta <P<s_H$. Infinite Schwarzschild time at crossing does not give infinitely many emitted pulses. The pulse phase $\delta$ fixes both the count and the redshift of the last pulse. If a finite pulse straddles the horizon, its exterior portion has an arbitrarily late, increasingly redshifted received tail.