docs: add activeHours to heartbeat field notes and examples (#9366)

Co-authored-by: unisone <unisone@users.noreply.github.com>

docs/gateway/heartbeat.md

@@ -137,6 +137,30 @@ Example: two agents, only the second agent runs heartbeats.
 }
 ```
 
+### Active hours example
+
+Restrict heartbeats to business hours in a specific timezone:
+
+```json5
+{
+  agents: {
+    defaults: {
+      heartbeat: {
+        every: "30m",
+        target: "last",
+        activeHours: {
+          start: "09:00",
+          end: "22:00",
+          timezone: "America/New_York", // optional; uses your userTimezone if set, otherwise host tz
+        },
+      },
+    },
+  },
+}
+```
+
+Outside this window (before 9am or after 10pm Eastern), heartbeats are skipped. The next scheduled tick inside the window will run normally.
+
 ### Multi account example
 
 Use `accountId` to target a specific account on multi-account channels like Telegram:
@@ -183,6 +207,11 @@ Use `accountId` to target a specific account on multi-account channels like Tele
 - `accountId`: optional account id for multi-account channels. When `target: "last"`, the account id applies to the resolved last channel if it supports accounts; otherwise it is ignored. If the account id does not match a configured account for the resolved channel, delivery is skipped.
 - `prompt`: overrides the default prompt body (not merged).
 - `ackMaxChars`: max chars allowed after `HEARTBEAT_OK` before delivery.
+- `activeHours`: restricts heartbeat runs to a time window. Object with `start` (HH:MM, inclusive), `end` (HH:MM exclusive; `24:00` allowed for end-of-day), and optional `timezone`.
+  - Omitted or `"user"`: uses your `agents.defaults.userTimezone` if set, otherwise falls back to the host system timezone.
+  - `"local"`: always uses the host system timezone.
+  - Any IANA identifier (e.g. `America/New_York`): used directly; if invalid, falls back to the `"user"` behavior above.
+  - Outside the active window, heartbeats are skipped until the next tick inside the window.
 
 ## Delivery behavior