http: make timeout event work with agent timeout

lib/_http_client.js

@@ -653,7 +653,10 @@ function tickOnSocket(req, socket) {
   socket.on('end', socketOnEnd);
   socket.on('close', socketCloseListener);
 
-  if (req.timeout !== undefined) {
+  if (
+    req.timeout !== undefined ||
+    (req.agent && req.agent.options && req.agent.options.timeout)
+  ) {
     listenSocketTimeout(req);
   }
   req.emit('socket', socket);

test/parallel/test-http-agent-timeout-option.js

@@ -0,0 +1,23 @@
+'use strict';
+
+const { expectsError, mustCall } = require('../common');
+const { Agent, get } = require('http');
+
+// Test that the `'timeout'` event is emitted on the `ClientRequest` instance
+// when the socket timeout set via the `timeout` option of the `Agent` expires.
+
+const request = get({
+  agent: new Agent({ timeout: 500 }),
+  // Non-routable IP address to prevent the connection from being established.
+  host: '192.0.2.1'
+});
+
+request.on('error', expectsError({
+  type: Error,
+  code: 'ECONNRESET',
+  message: 'socket hang up'
+}));
+
+request.on('timeout', mustCall(() => {
+  request.abort();
+}));