diff --git a/src/cmd/go/internal/modload/import.go b/src/cmd/go/internal/modload/import.go
index ce5671728e..c16531e2f4 100644
--- a/src/cmd/go/internal/modload/import.go
+++ b/src/cmd/go/internal/modload/import.go
@@ -58,7 +58,7 @@ func (e *ImportMissingError) Error() string {
 		if e.QueryErr != nil {
 			return fmt.Sprintf("cannot find module providing package %s: %v", e.Path, e.QueryErr)
 		}
-		if cfg.BuildMod == "mod" {
+		if cfg.BuildMod == "mod" || (cfg.BuildMod == "readonly" && allowMissingModuleImports) {
 			return "cannot find module providing package " + e.Path
 		}
 
@@ -365,7 +365,7 @@ func queryImport(ctx context.Context, path string) (module.Version, error) {
 		return module.Version{}, &ImportMissingError{Path: path, isStd: true}
 	}
 
-	if cfg.BuildMod == "readonly" {
+	if cfg.BuildMod == "readonly" && !allowMissingModuleImports {
 		// In readonly mode, we can't write go.mod, so we shouldn't try to look up
 		// the module. If readonly mode was enabled explicitly, include that in
 		// the error message.
@@ -547,7 +547,7 @@ func fetch(ctx context.Context, mod module.Version, needSum bool) (dir string, i
 		mod = r
 	}
 
-	if cfg.BuildMod == "readonly" && needSum && !modfetch.HaveSum(mod) {
+	if HasModRoot() && cfg.BuildMod == "readonly" && needSum && !modfetch.HaveSum(mod) {
 		return "", false, module.VersionError(mod, &sumMissingError{})
 	}
 
diff --git a/src/cmd/go/internal/modload/import_test.go b/src/cmd/go/internal/modload/import_test.go
index 22d5b82e21..9420dc5646 100644
--- a/src/cmd/go/internal/modload/import_test.go
+++ b/src/cmd/go/internal/modload/import_test.go
@@ -58,10 +58,15 @@ var importTests = []struct {
 func TestQueryImport(t *testing.T) {
 	testenv.MustHaveExternalNetwork(t)
 	testenv.MustHaveExecPath(t, "git")
-	defer func(old bool) {
-		allowMissingModuleImports = old
-	}(allowMissingModuleImports)
-	AllowMissingModuleImports()
+
+	oldAllowMissingModuleImports := allowMissingModuleImports
+	oldRootMode := RootMode
+	defer func() {
+		allowMissingModuleImports = oldAllowMissingModuleImports
+		RootMode = oldRootMode
+	}()
+	allowMissingModuleImports = true
+	RootMode = NoRoot
 
 	ctx := context.Background()
 
diff --git a/src/cmd/go/internal/modload/init.go b/src/cmd/go/internal/modload/init.go
index 445ebb262f..b0acb7b25d 100644
--- a/src/cmd/go/internal/modload/init.go
+++ b/src/cmd/go/internal/modload/init.go
@@ -202,6 +202,8 @@ func Init() {
 	}
 
 	// We're in module mode. Set any global variables that need to be set.
+	cfg.ModulesEnabled = true
+	setDefaultBuildMod()
 	list := filepath.SplitList(cfg.BuildContext.GOPATH)
 	if len(list) == 0 || list[0] == "" {
 		base.Fatalf("missing $GOPATH")
@@ -211,8 +213,6 @@ func Init() {
 		base.Fatalf("$GOPATH/go.mod exists but should not")
 	}
 
-	cfg.ModulesEnabled = true
-
 	if modRoot == "" {
 		// We're in module mode, but not inside a module.
 		//
@@ -348,8 +348,8 @@ func die() {
 // ensuring requirements are consistent. WriteGoMod should be called later to
 // write changes out to disk or report errors in readonly mode.
 //
-// As a side-effect, LoadModFile sets a default for cfg.BuildMod if it does not
-// already have an explicit value.
+// As a side-effect, LoadModFile may change cfg.BuildMod to "vendor" if
+// -mod wasn't set explicitly and automatic vendoring should be enabled.
 func LoadModFile(ctx context.Context) {
 	if len(buildList) > 0 {
 		return
@@ -387,7 +387,7 @@ func LoadModFile(ctx context.Context) {
 		base.Fatalf("go: %v", err)
 	}
 
-	setDefaultBuildMod()
+	setDefaultBuildMod() // possibly enable automatic vendoring
 	modFileToBuildList()
 	if cfg.BuildMod == "vendor" {
 		readVendorList()
@@ -586,8 +586,8 @@ func modFileToBuildList() {
 	buildList = list
 }
 
-// setDefaultBuildMod sets a default value for cfg.BuildMod
-// if it is currently empty.
+// setDefaultBuildMod sets a default value for cfg.BuildMod if the -mod flag
+// wasn't provided. setDefaultBuildMod may be called multiple times.
 func setDefaultBuildMod() {
 	if cfg.BuildModExplicit {
 		// Don't override an explicit '-mod=' argument.
@@ -608,7 +608,7 @@ func setDefaultBuildMod() {
 
 	if fi, err := fsys.Stat(filepath.Join(modRoot, "vendor")); err == nil && fi.IsDir() {
 		modGo := "unspecified"
-		if index.goVersionV != "" {
+		if index != nil && index.goVersionV != "" {
 			if semver.Compare(index.goVersionV, "v1.14") >= 0 {
 				// The Go version is at least 1.14, and a vendor directory exists.
 				// Set -mod=vendor by default.
diff --git a/src/cmd/go/internal/modload/modfile.go b/src/cmd/go/internal/modload/modfile.go
index eb05e9f9c9..d5a17236cd 100644
--- a/src/cmd/go/internal/modload/modfile.go
+++ b/src/cmd/go/internal/modload/modfile.go
@@ -446,7 +446,7 @@ func goModSummary(m module.Version) (*modFileSummary, error) {
 	if actual.Path == "" {
 		actual = m
 	}
-	if cfg.BuildMod == "readonly" && actual.Version != "" {
+	if HasModRoot() && cfg.BuildMod == "readonly" && actual.Version != "" {
 		key := module.Version{Path: actual.Path, Version: actual.Version + "/go.mod"}
 		if !modfetch.HaveSum(key) {
 			suggestion := fmt.Sprintf("; try 'go mod download %s' to add it", m.Path)
diff --git a/src/cmd/go/testdata/script/mod_install_pkg_version.txt b/src/cmd/go/testdata/script/mod_install_pkg_version.txt
index e4a7668351..93896d4593 100644
--- a/src/cmd/go/testdata/script/mod_install_pkg_version.txt
+++ b/src/cmd/go/testdata/script/mod_install_pkg_version.txt
@@ -175,6 +175,11 @@ stdout '^\tmod\texample.com/cmd\tv1.0.0\t'
 go install example.com/cmd/a@v1.9.0
 go version -m $GOPATH/bin/a$GOEXE
 stdout '^\tmod\texample.com/cmd\tv1.9.0\t'
+env GO111MODULE=
+
+# 'go install pkg@version' succeeds when -mod=readonly is set explicitly.
+# Verifies #43278.
+go install -mod=readonly example.com/cmd/a@v1.0.0
 
 -- m/go.mod --
 module m