Merge request dropped from merge train with “No stages / jobs for this pipeline.”

When I click Start merge train on a merge request (MR), GitLab adds the following to the MR's system notes:

@sferencik started a merge train just now

Great. However, seconds later the following is added to the system notes:

@sferencik removed this merge request from the merge train because No stages / jobs for this pipeline. just now

[emphasis mine]

The list of pipelines doesn't have a new entry: the merge train didn't even get as far as starting one.

The GitLab documentation touches on this. This GitLab issue also talks about this, though in a different context.

What am I doing wrong? I have cut down my .gitlab-ci.yml to the bare minimum, leaving only one stage with one job, which is not conditional. It beats me why GitLab, having performed the speculative merge, should create a pipeline with "no stages / jobs."

This is not a build issue: by the time I click Start merge train, a pipeline has succeeded on my feature branch (the one I want to merge).

Also, if I switch off pipelines for merge results, my MRs have a Merge button instead of Start merge train and it works just fine.

This started happening with our upgrade from GitLab 12.0 to 12.1.

I've already posted this on StackOverflow, but I'm starting to suspect this may need your support directly.