AWS: How to specify a boolean parameter in a CloudFormation template

The Quick Start templates are a good, semi-official reference point of how complex templates can/should be created, and they implement Boolean values for Conditional resources exactly as you described, using a String with AllowedValues true and false. Here's a specific example:

"EnableBanner": {
"AllowedValues": [
"true",
"false"
],
"Default": "false",
"Description": "To include a banner to be displayed when connecting via SSH to the bastion, set this parameter to true",
"Type": "String"
}

A similar example can be found in the Conditionally use an existing resource example from the CloudFormation documentation, where the AllowedValues are default or NONE (the default).

To conditionally create a resource based on such a boolean parameter, you add a Condition statement containing a Fn::Equals intrinsic function matching true, then add a Condition key to the resource.

Here's a complete, minimal example template:

Parameters:
CreateResource:
Description: Whether I should create a resource.
Default: false
Type: String
AllowedValues: [true, false]
Conditions:
ShouldCreateResource:
!Equals [true, !Ref CreateResource]
Resources:
Resource:
Type: AWS::CloudFormation::WaitConditionHandle
Condition: ShouldCreateResource