Showing all-day or non-timed events in a task list

I have a timeline-like view (I don't want to call it a timeline because it is more like a list of work items).

Things you need to know

  • It's designed to show a quick overview of the recent activities.
  • Each vertical line is a list of tasks representing a team that the supervisor is responsible for (and they all need to be shown together). The colored ones have already been done (the colors represent success/failure/stopped, etc.)
  • The order of the tasks is based on time (not seen in the screenshot). Each card is a task and there are no overlapping tasks.
  • The grey line represents current time.

It looks something like this (orientation can be changed)

Work items for each line

My question

The timed tasks are easy to show as there is a time attached to them. But there are some tasks that just need to be done in the day but do not have a specific time attached to them (much like all day events in a calendar)

My issue is that I can't have a calendar/agenda view given the need of showing multiple lines.

How do I show non-timed tasks?

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