Actually something's not quite right.
Firstly, the configuration in the Multibranch project to "Trigger builds remotely" disappears after I save. Select the option, put a token, save and reopen. They are gone.
Secondly, assuming the configuration is actually saved, the url to trigger the build needs to have the branch name in it:
<jenkins_url>/job/<job name>/branch/master/build?token=some token
This actually works (despite the config seemingly not being saved). But without the branch name in the url it doesn't do anything. So do I have to setup a different webhook for each branch?
It feels like this should work out of the box and I'm doing something very silly.
And yet, invoking the url with curl triggers the build. Seems like a UI problem.