For your scenario, there are two separate paths through your pipeline depending on the "source": a 'push' or a 'schedule'. You can get the source of the pipeline with the CI_PIPELINE_SOURCE variable. I build these paths separately at first, then combine them:

# First source: push events
stages:
  build
  deploy
  test

variables:
    BUILD_ARTIFACTS_DIR: "artifacts"

build-incremental:
    timeout: 5h 
    stage: build
    script:
        - echo "Building"
        - ./ci/do-prep
        - echo "done."
    artifacts:
        paths:
            - $BUILD_ARTIFACTS_DIR/
    variables:
        BUILD_TOP_DIR: "/workspace/builds"
    tags:
        - yocto
    rules:
      - if: $CI_PIPELINE_SOURCE == 'push'
        when: manual
      - when: never

deploy-incremental:
    stage: deploy
    script:
        - echo "Deploying..."
        - ./ci/do-deploy
        - echo "done."
    tags:
        - yocto
    needs: ['build-incremental']
    rules:
      - if $CI_PIPELINE_SOURCE == 'push'
        when: always
      - when: never

test-incremental:
    stage: test
    script:
        - echo "Testing..."
        - ./ci/do-test
        - echo "done."
    tags:
        - yocto
    needs: ['deploy-incremental']
    rules:
      - if: $CI_PIPELINE_SOURCE == 'push'
        when: always
      - when: never

In this path, if the source is a push, the build step will run upon manual input, otherwise it will never run. Then, the deploy-incremental step will run automatically (without waiting for other jobs or stages) as long as the source is a push, otherwise it will never run. Finally the test-incremental job will run automatically without waiting for other jobs or stages if it's a push like above.

Now we can build the schedule path:

# Scheduled path:

stages:
  build
  deploy
  test

variables:
    BUILD_ARTIFACTS_DIR: "artifacts"

build-schedule:
    timeout: 5h 
    stage: build
    script:
        - echo "Building"
        - ./ci/do-prep
        - echo "done."
    artifacts:
        paths:
            - $BUILD_ARTIFACTS_DIR/
    variables:
        BUILD_TOP_DIR: "/workspace/builds"
    tags:
        - yocto
    rules:
      - if: $CI_PIPELINE_SOURCE === 'schedule'
        when: manual
      - when: never

deploy-schedule:
    stage: deploy
    script:
        - echo "Deploying..."
        - ./ci/do-deploy
        - echo "done."
    tags:
        - yocto
    needs: ['build-schedule']
    rules:
      - if $CI_PIPELINE_SOURCE == 'schedule'
        when: always
      - when: never

test-schedule:
    stage: test
    script:
        - echo "Testing..."
        - ./ci/do-test
        - echo "done."
    tags:
        - yocto
    needs: ['deploy-schedule']
    rules:
      - if: $CI_PIPELINE_SOURCE == 'schedule'
        when: always
      - when: never

This works the same way as the push path, but we check to see if the source is schedule.

Now we can combine the two paths:

Combined result:
stages:
  build
  deploy
  test

variables:
    BUILD_ARTIFACTS_DIR: "artifacts"

build-incremental:
    timeout: 5h 
    stage: build
    script:
        - echo "Building"
        - ./ci/do-prep
        - echo "done."
    artifacts:
        paths:
            - $BUILD_ARTIFACTS_DIR/
    variables:
        BUILD_TOP_DIR: "/workspace/builds"
    tags:
        - yocto
    rules:
      - if: $CI_PIPELINE_SOURCE == 'push'
        when: manual
      - when: never

build-schedule:
    timeout: 5h 
    stage: build
    script:
        - echo "Building"
        - ./ci/do-prep
        - echo "done."
    artifacts:
        paths:
            - $BUILD_ARTIFACTS_DIR/
    variables:
        BUILD_TOP_DIR: "/workspace/builds"
    tags:
        - yocto
    rules:
      - if: $CI_PIPELINE_SOURCE == 'schedule'
        when: manual
      - when: never

deploy-incremental:
    stage: deploy
    script:
        - echo "Deploying..."
        - ./ci/do-deploy
        - echo "done."
    tags:
        - yocto
    needs: ['build-incremental']
    rules:
      - if $CI_PIPELINE_SOURCE == 'push'
        when: always
      - when: never

deploy-schedule:
    stage: deploy
    script:
        - echo "Deploying..."
        - ./ci/do-deploy
        - echo "done."
    tags:
        - yocto
    needs: ['build-schedule']
    rules:
      - if $CI_PIPELINE_SOURCE == 'schedule'
        when: always
      - when: never

test-incremental:
    stage: test
    script:
        - echo "Testing..."
        - ./ci/do-test
        - echo "done."
    tags:
        - yocto
    needs: ['deploy-incremental']
    rules:
      - if: $CI_PIPELINE_SOURCE == 'push'
        when: always
      - when: never

test-schedule:
    stage: test
    script:
        - echo "Testing..."
        - ./ci/do-test
        - echo "done."
    tags:
        - yocto
    needs: ['deploy-schedule']
    rules:
      - if: $CI_PIPELINE_SOURCE == 'schedule'
        when: always
      - when: never

A pipeline like this is tedious and takes a bit to build, but works great when you have multiple paths/ways to build the project.

artifacts from all previous stages are passed by default

Means just that. By default you get all the dependencies. However there are times when you don't want all of them. For example if the last step in your pipe is sending a notification to slackchat you don't want to download hundreds of megabytes of artifacts just to do that.

In principle, if a job declares a needs statement then this job,in order to execute, it has to wait for the jobs that were referred in the statement to finish, even if they are in the same stage

In your case run-tests should wait for the build-test-image.

If you are on a self hosted check your Gitlab version

https://your.domain.com/help

The functionality you need was added in 14.2