Based on the FortiOS 7.6 Infrastructure and IPsec VPN documentation, Dead Peer Detection (DPD) can be configured in three primary modes: On Demand, On Idle, and Disabled.

On Demand (Default Mode): This mode is specifically designed to minimize unnecessary traffic. In this mode, FortiGate sends DPD probes only when there is no inbound traffic but the FortiGate is attempting to send outbound traffic. Because network communication is typically bidirectional, the absence of inbound traffic while outbound traffic is being sent is a primary indicator of a potentially dead tunnel. This matches the specific requirement described in the question.

On Idle: In this mode, DPD probes are sent if no traffic (neither inbound nor outbound) has been observed in the tunnel for a specific period. It verifies the tunnel status even when the connection is completely idle.

Enabled: In older versions or specific CLI contexts, "Enabled" may refer to periodic DPD, but in the current FortiOS 7.x/7.6 GUI and CLI terminology for Phase 1 settings, the active modes are defined as on-demand or on-idle.

Disabled: In this mode, the FortiGate does not send DPD probes but will still respond to DPD probes sent by the remote peer.

The requirement that the administrator wants probes sent only when there is no inbound traffic (usually implying the FortiGate is sending but not receiving) is the fundamental definition of the On Demand mechanism in the Fortinet curriculum.