diff --git a/x-pack/plugin/core/src/test/java/org/elasticsearch/xpack/core/ssl/SSLConfigurationReloaderTests.java b/x-pack/plugin/core/src/test/java/org/elasticsearch/xpack/core/ssl/SSLConfigurationReloaderTests.java
index 9202207a14e0f..3e36550e46f2b 100644
--- a/x-pack/plugin/core/src/test/java/org/elasticsearch/xpack/core/ssl/SSLConfigurationReloaderTests.java
+++ b/x-pack/plugin/core/src/test/java/org/elasticsearch/xpack/core/ssl/SSLConfigurationReloaderTests.java
@@ -78,6 +78,7 @@ public void cleanup() throws Exception {
     /**
      * Tests reloading a keystore that is used in the KeyManager of SSLContext
      */
+    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/32124")
     public void testReloadingKeyStore() throws Exception {
         assumeFalse("Can't run in a FIPS JVM", inFipsJvm());
         final Path tempDir = createTempDir();
@@ -191,6 +192,7 @@ public void testPEMKeyConfigReloading() throws Exception {
      * Tests the reloading of SSLContext when the trust store is modified. The same store is used as a TrustStore (for the
      * reloadable SSLContext used in the HTTPClient) and as a KeyStore for the MockWebServer
      */
+    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/32124")
     public void testReloadingTrustStore() throws Exception {
         assumeFalse("Can't run in a FIPS JVM", inFipsJvm());
         Path tempDir = createTempDir();
@@ -477,9 +479,7 @@ private static MockWebServer getSslServer(Path keyStorePath, String keyStorePass
         try (InputStream is = Files.newInputStream(keyStorePath)) {
             keyStore.load(is, keyStorePass.toCharArray());
         }
-        // TODO Revisit TLS1.2 pinning when TLS1.3 is fully supported
-        // https://github.com/elastic/elasticsearch/issues/32276
-        final SSLContext sslContext = new SSLContextBuilder().useProtocol("TLSv1.2").loadKeyMaterial(keyStore, keyStorePass.toCharArray())
+        final SSLContext sslContext = new SSLContextBuilder().loadKeyMaterial(keyStore, keyStorePass.toCharArray())
             .build();
         MockWebServer server = new MockWebServer(sslContext, false);
         server.enqueue(new MockResponse().setResponseCode(200).setBody("body"));
@@ -493,9 +493,7 @@ private static MockWebServer getSslServer(Path keyPath, Path certPath, String pa
         keyStore.load(null, password.toCharArray());
         keyStore.setKeyEntry("testnode_ec", PemUtils.readPrivateKey(keyPath, password::toCharArray), password.toCharArray(),
             CertParsingUtils.readCertificates(Collections.singletonList(certPath)));
-        // TODO Revisit TLS1.2 pinning when TLS1.3 is fully supported
-        // https://github.com/elastic/elasticsearch/issues/32276
-        final SSLContext sslContext = new SSLContextBuilder().useProtocol("TLSv1.2").loadKeyMaterial(keyStore, password.toCharArray())
+        final SSLContext sslContext = new SSLContextBuilder().loadKeyMaterial(keyStore, password.toCharArray())
             .build();
         MockWebServer server = new MockWebServer(sslContext, false);
         server.enqueue(new MockResponse().setResponseCode(200).setBody("body"));
@@ -510,7 +508,7 @@ private static CloseableHttpClient getSSLClient(Path trustStorePath, String trus
         try (InputStream is = Files.newInputStream(trustStorePath)) {
             trustStore.load(is, trustStorePass.toCharArray());
         }
-        final SSLContext sslContext = new SSLContextBuilder().useProtocol("TLSv1.2").loadTrustMaterial(trustStore, null).build();
+        final SSLContext sslContext = new SSLContextBuilder().loadTrustMaterial(trustStore, null).build();
         return HttpClients.custom().setSSLContext(sslContext).build();
     }
 
@@ -527,7 +525,7 @@ private static CloseableHttpClient getSSLClient(List<Path> trustedCertificatePat
         for (Certificate cert : CertParsingUtils.readCertificates(trustedCertificatePaths)) {
             trustStore.setCertificateEntry(cert.toString(), cert);
         }
-        final SSLContext sslContext = new SSLContextBuilder().useProtocol("TLSv1.2").loadTrustMaterial(trustStore, null).build();
+        final SSLContext sslContext = new SSLContextBuilder().loadTrustMaterial(trustStore, null).build();
         return HttpClients.custom().setSSLContext(sslContext).build();
     }