diff --git a/frontend/src/customer/AuthForm.tsx b/frontend/src/customer/AuthForm.tsx
index b357f35..2f1b51f 100644
--- a/frontend/src/customer/AuthForm.tsx
+++ b/frontend/src/customer/AuthForm.tsx
@@ -233,6 +233,27 @@ export default function AuthForm({ mode, onModeChange, onForgotPassword, onSucce
                   By creating an account you agree to our{' '}
                   <a href="/privacy" target="_blank" rel="noopener noreferrer">Privacy Policy</a>.
                 </Text>
+
+                {/* On this tab too, and its absence here was a bug (#345).
+                    A passkey belongs only on Log In, because you cannot
+                    register an account with one — but creating an account is
+                    exactly what a new customer reaches for Google to do, so
+                    leaving it off the sign-up tab hid the feature from the
+                    people it helps most.
+
+                    The two consent boxes above are not carried across. Google
+                    takes the customer off this site entirely, and a tick that
+                    survived that round trip would be a consent recorded from a
+                    form nobody submitted. They are asked again, with the same
+                    wording, on the step they land on (#342). */}
+                {googleEnabled && (
+                  <>
+                    <Divider plain style={{ marginBlock: 16 }}>
+                      <Text type="secondary" style={{ fontSize: 12 }}>or</Text>
+                    </Divider>
+                    <GoogleSignInButton returnTo={returnTo} intent="sign-up" />
+                  </>
+                )}
               </Form>
             )
           },
diff --git a/frontend/src/customer/GoogleSignInButton.tsx b/frontend/src/customer/GoogleSignInButton.tsx
index 4ce5d4b..9cddcb9 100644
--- a/frontend/src/customer/GoogleSignInButton.tsx
+++ b/frontend/src/customer/GoogleSignInButton.tsx
@@ -37,6 +37,17 @@ function GoogleMark() {
 type Props = Readonly<{
   /** Where to send the customer back to. Validated again on the server. */
   returnTo: string;
+  /**
+   * Which tab this sits on, which changes only the wording.
+   *
+   * One endpoint serves both: it signs in a known identity, links a verified
+   * address, or creates an account. The customer does not know or care which
+   * of those will happen, so the label matches what they came to the tab to
+   * do rather than what the server ends up doing.
+   *
+   * Both spellings are in Google identity guidelines alongside the mark.
+   */
+  intent?: 'sign-in' | 'sign-up';
 }>;
 
 /**
@@ -51,7 +62,7 @@ type Props = Readonly<{
  * here. It has to be, since anyone can type the URL, and doing it in one place
  * beats doing it in two languages. See `google/returnTo.ts`.
  */
-export default function GoogleSignInButton({ returnTo }: Props) {
+export default function GoogleSignInButton({ returnTo, intent = 'sign-in' }: Props) {
   return (
     <Button
       block
@@ -62,7 +73,7 @@ export default function GoogleSignInButton({ returnTo }: Props) {
         window.location.assign(`/api/auth/google/start?returnTo=${encodeURIComponent(returnTo)}`);
       }}
     >
-      Sign in with Google
+      {intent === 'sign-up' ? 'Sign up with Google' : 'Sign in with Google'}
     </Button>
   );
 }
diff --git a/frontend/tests/e2e/auth.spec.ts b/frontend/tests/e2e/auth.spec.ts
index 2cd733d..7abb059 100755
--- a/frontend/tests/e2e/auth.spec.ts
+++ b/frontend/tests/e2e/auth.spec.ts
@@ -124,6 +124,23 @@ test.describe('Customer accounts', () => {
   // So the button being ABSENT is the behaviour under test here, and it is the
   // one that matters: a control that appears and then fails at Google is worse
   // than one that was never offered.
+  // The sign-up tab, which #345 left it off entirely. A passkey belongs only on
+  // Log In, because you cannot register an account with one — but creating an
+  // account is exactly what a new customer reaches for Google to do, so its
+  // absence there hid the feature from the people it helps most.
+  //
+  // Asserted as absent for the same reason as the login one: local and QA have
+  // no credentials, so absence is the behaviour that actually runs here.
+  test('offers no Google button on the sign-up tab either, when unconfigured', async ({
+    authModal
+  }) => {
+    await authModal.gotoRegister();
+
+    await expect(
+      authModal.registerDialog.getByRole('button', { name: /with Google/i })
+    ).toHaveCount(0);
+  });
+
   test('offers no Google button when the environment is not configured for it', async ({
     authModal,
     accountModal,