How do I successfully peer two VPCs using transit gateway?

I am trying to peer two VPCs through a transit gateway, but I am having trouble making a connection from a pod in VPC_1 to VPC_2's RDS instance.

• VPC_1 has a cluster with an RDS instance (MySQL).
• VPC_2 has a cluster for which node groups must be able to connect to the RDS instance.

I ensured the following:

• There is a transit gateway attachment between the transit gateway and VPC_1, and VPC_2. So they are both attached to the same transit gateway.
• There is an inbound security group rule in the RDS instance allowing traffic from VPC_2's IP address range on port 3306.

I spun up a pod inside VPC_2's EKS cluster and attempted to connect to the RDS instance of VPC_1, but I was unable to connect. I am not sure what could be missing here, I am thinking perhaps some route tables or some security group rules. But from my understanding, the configuration that I have should be enough to achieve connectivity.

Can someone please help guide me, or give me some pointers on what I could be missing?

I have tried the following:

• Using the AWS connectivity analyzer to check if the connection between the 2 VPCs is fine. It says it's good but I don't always trust it.