I created simple pipeline called mytrigger.yaml with the name of mytrigger in Azure DevOps.

trigger:
  branches:
    include:
      - test/pipeline

pool:
  vmImage: ubuntu-latest

steps:
- script: echo Hello, world!
  displayName: 'Run a one-line script'

- script: |
    echo Add other tasks to build, test, and deploy your project.
    echo See https://aka.ms/yaml
  displayName: 'Run a multi-line script'

And the second one called bytrigger.yaml with the name of bytrigger in Azure DevOps.

pool:
  vmImage: ubuntu-latest

resources:
  pipelines:
  - pipeline: mySourcePipeline
    source: 'mytrigger'
    trigger:
      branches:
        include:
          - test/pipeline

steps:
- script: |
    echo Add other tasks to build, test, and deploy your project.
    echo See https://aka.ms/yaml
  displayName: 'Run a multi-line script'

I tried both the yaml and classic mode method to finalize that task, however in both cases when I run mytrigger pipeline and go back to the Pipelines section on Azure DevOps I do not see that by trigger pipeline starts working after mytrigger succesfully was finished.

As you can see both are in the test/pipeline branch.

Independently both pipelines work, so my expectation is to trigger the bytrigger pipeline by mytrigger pipeline.