Why does debugging break access to an AWS::Lamba::LayerVersion when using "sam invoke local"?

This works:

sam local invoke -t template.local.yaml -e events/event-timezone.json GetTimezoneFunction

This does not work when trying to debug with Visual Studio Code:

sam local invoke -t template.local.yaml -e events/event-timezone.json -d 5858 GetTimezoneFunction

The difference is that, in the second, I get an error that the npm 'axios' module, which is defined in a separate layer used by my lambda function, is not found.

Error: Cannot find module 'axios'
Require stack:
 - /var/task/get-timezone.js
 - /var/runtime/UserFunction.js
 - /var/runtime/index.js

All I can figure is that maybe by trying to use the debugger either the resources of the layer aren't copied to the Docker runtime environment, or some file search path gets broken.

I have another lambda function which doesn't need anything from the layer, and works fine with or without the debugger.

The file with the getTimeZone function starts with:

import axios from 'axios';

This is the relevant part of template.local.yaml:

AWSTemplateFormatVersion: '2010-09-09'
Transform: AWS::Serverless-2016-10-31
Description: AWS Sample

Globals:
  Function:
    Timeout: 30

Resources:
  SampleCommonLayer:
    Type: AWS::Lambda::LayerVersion
    Properties:
      CompatibleRuntimes:
        - nodejs12.x
      Content: dependencies
      Description: Sample Common LayerVersion
      LayerName: SampleCommonLayer

  GetTimezoneFunction:
    Type: AWS::Serverless::Function
    Properties:
      CodeUri: dist/get-timezone
      Handler: get-timezone.getTimezone
      Runtime: nodejs12.x
      Layers:
        - !Ref SampleCommonLayer
      Events:
        GetTimezone:
          Type: Api
          Properties:
            Path: /get-timezone
            Method: get

Outputs:
  GetTimezoneApi:
    Description: "API Gateway endpoint URL for Prod stage for getTimezone function"
    Value: !Sub "https://${ServerlessRestApi}.execute-api.${AWS::Region}.amazonaws.com/Prod/get-timezone/"
  GetTimezoneFunction:
    Description: "getTimezone Lambda Function ARN"
    Value: !GetAtt GetTimezoneFunction.Arn
  GetTimezoneFunctionIamRole:
    Description: "Implicit IAM Role created for getTimezone function"
    Value: !GetAtt GetTimezoneFunctionRole.Arn

Here's my launch.json:

{
  "version": "0.2.0",
  "configurations": [{
      "name": "Debug get-timezone",
      "type": "node",
      "request": "attach",
      "address": "localhost",
      "port": 5858,
      "localRoot": "${workspaceRoot}/dist",
      "remoteRoot": "/var/task",
      "protocol": "inspector",
      "stopOnEntry": false,
      "preLaunchTask": "local-tz-debug"
    },
    ...
  ]
}

So far I've only found a lot of unanswered questions and a few not-quite-the-same problems while searching for an answer to this problem.