As to the issue of the 403 error, that is likely due to IAM auth. How are you signing the connection request to Neptune?

Here’s an example of connecting via Gremlin-Javascript library with IAM signing. This fetches credentials using the Default Credential Provider Chain. In this case, that would be fetched from whatever is provided by the ECS task execution role.

const gremlin = require('gremlin');
const { fromNodeProviderChain } = require('@aws-sdk/credential-providers');
const {getUrlAndHeaders} = require('gremlin-aws-sigv4/lib/utils');
const __ = gremlin.process.statics;
const DriverRemoteConnection = gremlin.driver.DriverRemoteConnection;
const Graph = gremlin.structure.Graph;

const region = 'us-west-2';
const getCredentials = async () => {
    let credentials;
    try {
      credentials = fromNodeProviderChain({ clientConfig: { region }});
    } catch (e) {
      console.error("No credentials found", e);
    }
    return credentials;
  };

(main = async () => {
    console.log('starting');
    let provider = await getCredentials();
    let creds = await provider();
    creds['region'] = region;
    conninfo = getUrlAndHeaders(
        'neptune-cluster-endpoint.us-west-2.neptune.amazonaws.com',
        '8182',
        creds,
        '/gremlin',
        'wss'); 

    console.log(conninfo);

    dc = new DriverRemoteConnection(conninfo['url'], { headers: conninfo['headers'] });

    const graph = new Graph();
    const g = graph.traversal().withRemote(dc);

    query = g.V('some-id').valueMap(true);

    res = await query.next();

    console.log(res);

    dc.close();
})

main()

This is similar to what is documented as the example Node Lambda function in our docs (https://docs.aws.amazon.com/neptune/latest/userguide/lambda-functions-examples.html#lambda-functions-examples-javascript). That example is more comprehensive as it also provides means for handling connection errors and reconnects.