出现连接超时错误通常是由于网络配置或访问权限问题引起的。以下是解决方法的示例代码：

1. 确保VPC配置正确：

import boto3

# 创建EC2客户端
ec2 = boto3.client('ec2')

# 获取默认VPC ID
response = ec2.describe_vpcs()
vpc_id = response['Vpcs'][0]['VpcId']

# 更新Beanstalk环境的VPC配置
elasticbeanstalk = boto3.client('elasticbeanstalk')
response = elasticbeanstalk.update_environment(
    ApplicationName='your-application',
    EnvironmentName='your-environment',
    OptionSettings=[
        {
            'Namespace': 'aws:ec2:vpc',
            'OptionName': 'VPCId',
            'Value': vpc_id
        }
    ]
)

2. 确保安全组配置正确：

import boto3

# 创建EC2客户端
ec2 = boto3.client('ec2')

# 获取默认安全组ID
response = ec2.describe_security_groups()
security_group_id = response['SecurityGroups'][0]['GroupId']

# 更新Beanstalk环境的安全组配置
elasticbeanstalk = boto3.client('elasticbeanstalk')
response = elasticbeanstalk.update_environment(
    ApplicationName='your-application',
    EnvironmentName='your-environment',
    OptionSettings=[
        {
            'Namespace': 'aws:ec2:vpc',
            'OptionName': 'SecurityGroups',
            'Value': security_group_id
        }
    ]
)

3. 确保Beanstalk环境具有访问RDS的权限：

import boto3

# 创建IAM客户端
iam = boto3.client('iam')

# 创建Beanstalk服务角色策略
response = iam.create_policy(
    PolicyName='BeanstalkRDSAccessPolicy',
    PolicyDocument={
        "Version": "2012-10-17",
        "Statement": [
            {
                "Effect": "Allow",
                "Action": [
                    "rds:DescribeDBInstances",
                    "rds:DescribeDBClusters"
                ],
                "Resource": "*"
            }
        ]
    }
)

# 获取Beanstalk服务角色ARN
role_arn = iam.get_role(RoleName='aws-elasticbeanstalk-service-role')['Role']['Arn']

# 将策略附加到Beanstalk服务角色
response = iam.attach_role_policy(
    RoleName='aws-elasticbeanstalk-service-role',
    PolicyArn=response['Policy']['Arn']
)

请根据实际情况修改代码中的占位符，并确保您具有适当的AWS IAM权限执行这些操作。