Concepts like "days" only make sense with a day/night cycle, or if you have a race like humans who need sleep every 24 hours. So you're right, if there's no days, or no sleep, there's nothing to base your time on.
There is a place on earth with no day night cycle for parts of the year. Its discussed quite well on Wikipedia.
Basically they pick some place of importance (eg Greenwich England) and use the time there as their clock. (Technically they use UTC time, not GMT, but the difference is academic).
I would expect aliens in space to operate similar to humans in Antarctica, referencing their home planets clocks, even if they don't really make sense to their current day night cycle. They may be needed to help with a biological requirement (eg sleep), but if nothing else the ability to synchronise events "everyone be back from your mission by x" is a non negotiable. Not to mention its need for science and engineering work.
I'd expect aliens on a planet long term to derive at least a local calendar and clock to simplify life on that planet. But they'd probably choose to operate in their home time systems for anything like maths or physics.
Our Mars missions will use a custom clock to understand the conditions, but if were doing physics on the surface we'll be using old faithful metric earth seconds. If we change our time meanings we need to change measurements of energy, work, acceleration etc. Confusing this could be devastating.
A very large alien civilisation may create a galactic standard time or something. It's non trivial as the speed of light makes synchronisation provably impossible.
If we have no ftl, I'd suggest they base it on "spins of a pulsar" or something which can be observed galaxy wide. Technically events will never be in sync, "midnight" or a similar concept under the galactic calendar will propagate outwards like a wave travelling at the speed of light. The time day from the beacon will be used like our current time zones, eg "Earth is GST+707yrs."