Agent gets ringing sound in stead of getting busy or engage/beep sound when he makes a call while the customer is on another call. This is a Defect which needs to be addressed.

The issue you're describing is not actually a defect, but rather the default behavior of Amazon Connect when transferring calls. When an agent attempts to transfer a call to a number that is already engaged, the system typically continues to ring instead of providing a busy or engaged tone. This is because Amazon Connect doesn't have direct insight into the status of external phone lines.

However, there are a few potential solutions to address this situation:

1. Implement a callback option: This is a viable solution that Amazon Connect supports. You can set up a contact flow that offers customers the option to receive a callback from the same agent when they become available. This feature can be particularly useful in scenarios like employee transportation pick-ups and drop-offs, where connecting with a specific agent is important.

2. Modify the contact flow: You can adjust your contact flow to handle scenarios where the transfer doesn't connect immediately. For example, you could set a timeout for the transfer attempt and then route the call to an alternative destination or offer a callback option if the transfer isn't successful within a certain timeframe.

3. Use Amazon Connect's queuing system: Instead of transferring directly to an external number, you could set up a queue for each agent. This would allow you to better manage call distribution and provide more accurate information about agent availability.

4. Leverage custom attributes: You can use custom attributes to track agent status and availability. This could help prevent transfer attempts to agents who are already on calls.

5. Integrate with external systems: If you're using external phone systems, you might be able to integrate them with Amazon Connect using APIs or Amazon Chime Voice Connector to get more accurate information about line status.

Remember, implementing these solutions may require adjustments to your contact flows and possibly some custom development. It's recommended to thoroughly test any changes in a non-production environment before deploying them to your live system.

Sources
Amazon Connect rejected call still keeps ringing back | AWS re:Post
How to get rid of ringing tone while transferring call using Transfer To Phone Number from Amazon Connect Contact Flow to the External IVR Application | AWS re:Post
amazon_connect-flow | AWS re:Post