diff --git a/pkg/cmd/extension/command.go b/pkg/cmd/extension/command.go
index b19b80b55..50112b717 100644
--- a/pkg/cmd/extension/command.go
+++ b/pkg/cmd/extension/command.go
@@ -124,6 +124,9 @@ func NewCmdExtension(f *cmdutil.Factory) *cobra.Command {
 						} else if errors.Is(err, commitNotFoundErr) {
 							return fmt.Errorf("%s %s does not exist in %s",
 								cs.FailureIcon(), cs.Cyan(pinFlag), args[0])
+						} else if errors.Is(err, repositoryNotFoundErr) {
+							return fmt.Errorf("%s Could not find extension '%s' on host %s",
+								cs.FailureIcon(), args[0], repo.RepoHost())
 						}
 						return err
 					}
diff --git a/pkg/cmd/extension/command_test.go b/pkg/cmd/extension/command_test.go
index fb4707320..46bc109af 100644
--- a/pkg/cmd/extension/command_test.go
+++ b/pkg/cmd/extension/command_test.go
@@ -87,6 +87,25 @@ func TestNewCmdExtension(t *testing.T) {
 				}
 			},
 		},
+		{
+			name: "error extension not found",
+			args: []string{"install", "owner/gh-some-ext"},
+			managerStubs: func(em *extensions.ExtensionManagerMock) func(*testing.T) {
+				em.ListFunc = func() []extensions.Extension {
+					return []extensions.Extension{}
+				}
+				em.InstallFunc = func(_ ghrepo.Interface, _ string) error {
+					return repositoryNotFoundErr
+				}
+				return func(t *testing.T) {
+					installCalls := em.InstallCalls()
+					assert.Equal(t, 1, len(installCalls))
+					assert.Equal(t, "gh-some-ext", installCalls[0].InterfaceMoqParam.RepoName())
+				}
+			},
+			wantErr: true,
+			errMsg:  "X Could not find extension 'owner/gh-some-ext' on host github.com",
+		},
 		{
 			name:    "install local extension with pin",
 			args:    []string{"install", ".", "--pin", "v1.0.0"},
diff --git a/pkg/cmd/extension/http.go b/pkg/cmd/extension/http.go
index 5e3c23d69..2fae2f023 100644
--- a/pkg/cmd/extension/http.go
+++ b/pkg/cmd/extension/http.go
@@ -13,32 +13,54 @@ import (
 	"github.com/cli/cli/v2/internal/ghrepo"
 )
 
-func hasScript(httpClient *http.Client, repo ghrepo.Interface) (hs bool, err error) {
+func repoExists(httpClient *http.Client, repo ghrepo.Interface) (bool, error) {
+	url := fmt.Sprintf("%srepos/%s/%s", ghinstance.RESTPrefix(repo.RepoHost()), repo.RepoOwner(), repo.RepoName())
+	req, err := http.NewRequest("GET", url, nil)
+	if err != nil {
+		return false, err
+	}
+
+	resp, err := httpClient.Do(req)
+	if err != nil {
+		return false, err
+	}
+	defer resp.Body.Close()
+
+	switch resp.StatusCode {
+	case 200:
+		return true, nil
+	case 404:
+		return false, nil
+	default:
+		return false, api.HandleHTTPError(resp)
+	}
+}
+
+func hasScript(httpClient *http.Client, repo ghrepo.Interface) (bool, error) {
 	path := fmt.Sprintf("repos/%s/%s/contents/%s",
 		repo.RepoOwner(), repo.RepoName(), repo.RepoName())
 	url := ghinstance.RESTPrefix(repo.RepoHost()) + path
 	req, err := http.NewRequest("GET", url, nil)
 	if err != nil {
-		return
+		return false, err
 	}
 
 	resp, err := httpClient.Do(req)
 	if err != nil {
-		return
+		return false, err
 	}
 	defer resp.Body.Close()
 
 	if resp.StatusCode == 404 {
-		return
+		return false, nil
 	}
 
 	if resp.StatusCode > 299 {
 		err = api.HandleHTTPError(resp)
-		return
+		return false, err
 	}
 
-	hs = true
-	return
+	return true, nil
 }
 
 type releaseAsset struct {
@@ -80,8 +102,9 @@ func downloadAsset(httpClient *http.Client, asset releaseAsset, destPath string)
 	return err
 }
 
-var releaseNotFoundErr = errors.New("release not found")
 var commitNotFoundErr = errors.New("commit not found")
+var releaseNotFoundErr = errors.New("release not found")
+var repositoryNotFoundErr = errors.New("repository not found")
 
 // fetchLatestRelease finds the latest published release for a repository.
 func fetchLatestRelease(httpClient *http.Client, baseRepo ghrepo.Interface) (*release, error) {
@@ -98,6 +121,9 @@ func fetchLatestRelease(httpClient *http.Client, baseRepo ghrepo.Interface) (*re
 	}
 	defer resp.Body.Close()
 
+	if resp.StatusCode == 404 {
+		return nil, releaseNotFoundErr
+	}
 	if resp.StatusCode > 299 {
 		return nil, api.HandleHTTPError(resp)
 	}
@@ -162,7 +188,7 @@ func fetchCommitSHA(httpClient *http.Client, baseRepo ghrepo.Interface, targetRe
 		return "", err
 	}
 
-	req.Header.Set("Accept", "application/vnd.github.VERSION.sha")
+	req.Header.Set("Accept", "application/vnd.github.v3.sha")
 	resp, err := httpClient.Do(req)
 	if err != nil {
 		return "", err
diff --git a/pkg/cmd/extension/manager.go b/pkg/cmd/extension/manager.go
index 8ca79537d..289a9aefa 100644
--- a/pkg/cmd/extension/manager.go
+++ b/pkg/cmd/extension/manager.go
@@ -339,7 +339,15 @@ type binManifest struct {
 func (m *Manager) Install(repo ghrepo.Interface, target string) error {
 	isBin, err := isBinExtension(m.client, repo)
 	if err != nil {
-		return fmt.Errorf("could not check for binary extension: %w", err)
+		if errors.Is(err, releaseNotFoundErr) {
+			if ok, err := repoExists(m.client, repo); err != nil {
+				return err
+			} else if !ok {
+				return repositoryNotFoundErr
+			}
+		} else {
+			return fmt.Errorf("could not check for binary extension: %w", err)
+		}
 	}
 	if isBin {
 		return m.installBin(repo, target)
@@ -760,11 +768,6 @@ func isBinExtension(client *http.Client, repo ghrepo.Interface) (isBin bool, err
 	var r *release
 	r, err = fetchLatestRelease(client, repo)
 	if err != nil {
-		httpErr, ok := err.(api.HTTPError)
-		if ok && httpErr.StatusCode == 404 {
-			err = nil
-			return
-		}
 		return
 	}
 
diff --git a/pkg/cmd/extension/manager_test.go b/pkg/cmd/extension/manager_test.go
index e29dc0510..2dbd81870 100644
--- a/pkg/cmd/extension/manager_test.go
+++ b/pkg/cmd/extension/manager_test.go
@@ -844,6 +844,32 @@ func TestManager_Install_binary(t *testing.T) {
 	assert.Equal(t, "", stderr.String())
 }
 
+func TestManager_repo_not_found(t *testing.T) {
+	repo := ghrepo.NewWithHost("owner", "gh-bin-ext", "example.com")
+
+	reg := httpmock.Registry{}
+	defer reg.Verify(t)
+
+	reg.Register(
+		httpmock.REST("GET", "api/v3/repos/owner/gh-bin-ext/releases/latest"),
+		httpmock.StatusStringResponse(404, `{}`))
+	reg.Register(
+		httpmock.REST("GET", "api/v3/repos/owner/gh-bin-ext"),
+		httpmock.StatusStringResponse(404, `{}`))
+
+	ios, _, stdout, stderr := iostreams.Test()
+	tempDir := t.TempDir()
+
+	m := newTestManager(tempDir, &http.Client{Transport: &reg}, ios)
+
+	if err := m.Install(repo, ""); err != repositoryNotFoundErr {
+		t.Errorf("expected repositoryNotFoundErr, got: %v", err)
+	}
+
+	assert.Equal(t, "", stdout.String())
+	assert.Equal(t, "", stderr.String())
+}
+
 func TestManager_Create(t *testing.T) {
 	chdirTemp(t)
 	ios, _, stdout, stderr := iostreams.Test()