ImageId requried when launching instance via a Launch Template

The documentation (https://docs.aws.amazon.com/aws-sdk-php/v3/api/api-ec2-2016-11-15.html#runinstances) claims that I can either specify ImageId directly or via a launch template. But if I specify it in a launch template, the request fails validation. The SDK doesn't even make an outbound connection, just errors out immediately.

How can I make EC2 use the ImageId specified in my launch template?

I'm using the following code to launch an EC2 instance using a launch template:

        $result = $ec2->runInstances([
            'DryRun' => false,
            'LaunchTemplate' => [
                'LaunchTemplateName' => 'test-template',
                'Version' => 1
            ],
            'MinCount' => 1,
            'MaxCount' => 1
        ]);

The template ("test-template" Version 1) has an AMI specified (ami-086b3de06dafe36c5 - Amazon Linux 2). When I run the code above, I immediatelly get the following:

Found 1 error while validating the input provided for the RunInstances operation: [ImageId] is missing and is a required parameter