Ensure explicit `false` values from customize form get stored (#10381)

src/panels/config/customize/ha-config-customize.ts

@@ -25,7 +25,7 @@ class HaConfigCustomize extends LitElement {
   protected render(): TemplateResult {
     return html`
       <hass-tabs-subpage
-      .hass=${this.hass}
+        .hass=${this.hass}
         .narrow=${this.narrow}
         .route=${this.route}
         back-path="/config"

src/panels/config/customize/ha-form-customize.js

@@ -180,10 +180,16 @@ export class HaFormCustomize extends LocalizeMixin(PolymerElement) {
       this.newAttributes
     );
     attrs.forEach((attr) => {
-      if (attr.closed || attr.secondary || !attr.attribute || !attr.value)
+      if (
+        attr.closed ||
+        attr.secondary ||
+        !attr.attribute ||
+        attr.value === null ||
+        attr.value === undefined
+      )
         return;
       const value = attr.type === "json" ? JSON.parse(attr.value) : attr.value;
-      if (!value) return;
+      if (value === null || value === undefined) return;
       data[attr.attribute] = value;
     });