diff --git a/static/js/compose.js b/static/js/compose.js
index b009a1c15d..515978b390 100644
--- a/static/js/compose.js
+++ b/static/js/compose.js
@@ -615,11 +615,12 @@ export function initialize() {
         }
     });
 
-    let instance = {};
     $("body").on("click", ".time_pick", (e) => {
         e.preventDefault();
         e.stopPropagation();
 
+        $(e.target).toggleClass("has_popover");
+
         let target_textarea;
         let edit_message_id;
         const compose_click_target = compose_ui.get_compose_click_target(e);
@@ -630,13 +631,13 @@ export function initialize() {
             target_textarea = $(compose_click_target).closest("form").find("textarea");
         }
 
-        if (!instance.calendarContainer) {
+        if ($(e.target).hasClass("has_popover")) {
             const on_timestamp_selection = (val) => {
                 const timestr = `<time:${val}> `;
                 compose_ui.insert_syntax_and_focus(timestr, target_textarea);
             };
 
-            instance = composebox_typeahead.show_flatpickr(
+            composebox_typeahead.show_flatpickr(
                 $(compose_click_target)[0],
                 on_timestamp_selection,
                 new Date(),
@@ -645,11 +646,7 @@ export function initialize() {
                     position: "above center",
                 },
             );
-            return;
         }
-
-        instance.close();
-        instance.destroy();
     });
 
     $("#compose").on("click", ".markdown_preview", (e) => {
diff --git a/static/js/composebox_typeahead.js b/static/js/composebox_typeahead.js
index 585b825036..5f77a95a34 100644
--- a/static/js/composebox_typeahead.js
+++ b/static/js/composebox_typeahead.js
@@ -13,6 +13,7 @@ import * as compose_pm_pill from "./compose_pm_pill";
 import * as compose_state from "./compose_state";
 import * as compose_ui from "./compose_ui";
 import * as compose_validate from "./compose_validate";
+import {get_keydown_hotkey} from "./hotkey";
 import {$t} from "./i18n";
 import * as message_store from "./message_store";
 import * as muted_users from "./muted_users";
@@ -786,13 +787,66 @@ export function show_flatpickr(element, callback, default_timestamp, options = {
         dateFormat: "Z",
         formatDate: (date) => formatISO(date),
         disableMobile: true,
+        onKeyDown: (selectedDates, dateStr, instance, event) => {
+            const hotkey = get_keydown_hotkey(event);
+
+            if (["tab", "shift_tab"].includes(hotkey.name)) {
+                const elems = [
+                    instance.selectedDateElem,
+                    instance.hourElement,
+                    instance.minuteElement,
+                    instance.amPM,
+                    $(".flatpickr-confirm")[0],
+                ];
+                const i = elems.indexOf(event.target);
+                const n = elems.length;
+                const remain = (i + (event.shiftKey ? -1 : 1)) % n;
+                const target = elems[Math.floor(remain >= 0 ? remain : remain + n)];
+                event.preventDefault();
+                event.stopPropagation();
+                target.focus();
+            }
+
+            event.stopPropagation();
+        },
         ...options,
     });
 
     const container = $($(instance.innerContainer).parent());
-    container.on("click", ".flatpickr-calendar", (e) => {
+
+    container.on("keydown", (e) => {
+        const hotkey = get_keydown_hotkey(e);
+
+        if (!hotkey) {
+            return false;
+        }
+
+        if (hotkey.name === "enter") {
+            if (e.target.classList[0] === "flatpickr-day") {
+                return true; // use flatpickr default implementation
+            }
+            $(element).toggleClass("has_popover");
+            container.find(".flatpickr-confirm").trigger("click");
+        }
+
+        if (hotkey.name === "escape") {
+            $(element).toggleClass("has_popover");
+            instance.close();
+            instance.destroy();
+        }
+
+        if (["tab", "shift_tab"].includes(hotkey.name)) {
+            return true; // use flatpickr default implementation
+        }
+
+        if (["right_arrow", "up_arrow", "left_arrow", "down_arrow"].includes(hotkey.name)) {
+            return true; // use flatpickr default implementation
+        }
+
         e.stopPropagation();
         e.preventDefault();
+
+        return true;
     });
 
     container.on("click", ".flatpickr-confirm", () => {
@@ -801,7 +855,7 @@ export function show_flatpickr(element, callback, default_timestamp, options = {
         instance.destroy();
     });
     instance.open();
-    container.find(".flatpickr-monthDropdown-months").trigger("focus");
+    instance.selectedDateElem.focus();
 
     return instance;
 }