HTTP API Gateway - HTTP URI Integration fails when query contains spaces

I have an HTTP API Gateway with a "search" route that calls an external API via the HTTP URI integration type. I want to map the query string parameter "song" in my API to "q" in the external API, with a static prefix added. For example, GET /search?song=Yesterday should map to https://external-api/search?q=The+Beatles+-+Yesterday.

This works in my example above, but breaks if the original query contains a space (e.g., searching for Hey Jude instead of Yesterday).

The only workaround I have found is to URL encode the original query twice (e.g. calling my API with GET /search?song=Hey%2520Jude).

My current parameter mapping is as follows:

I've tried the following to no avail:

• + instead of %20
• Removing the prefix and just mapping q to $request.querystring.song
• Adding brackets (e.g., ${request.querystring.song})

I would like to be able to map GET /search?song=Hey%20Jude to https://external-api/search?q=The%20Beatles%20-%20Hey%20Jude without having to double-encode my input (as this would be annoying for people calling my API).