Which mode of operation would allows for time-shared use of a frequency?

The mode of operation that allows for time-shared use of a frequency is half-duplex. In half-duplex communication, both parties can transmit and receive but not simultaneously. This means that one party can send a signal at a time, which can be interspersed with periods when the other party responds. The alternating use of the frequency makes it possible for multiple users to share a frequency without interference, as they take turns communicating.

In contrast, full-duplex allows simultaneous two-way communication, which does not lend itself to time-sharing on a single frequency since both parties would be transmitting at the same time. Simplex only allows one-way communication, where one station transmits and the other only receives, thus not allowing time-sharing. While pulsed operation can refer to various transmission methods, it does not specifically relate to time-sharing a frequency in the same context as half-duplex.