Automatically reboot EC-2 linux servers of a target-group if OS update requires a reboot

We're having some Ubuntu instances that are registered targets of Target Groups behind an Elastic Load Balancer. Also, those servers make use of the "unattended-upgrades" package to install security relevant packages. Some of those newly installed packages require the server to be rebooted. Therefore it sends an email to our System Engineers to let them know.

So now, in order to reboot those instances they need to be deregistered from their Target Group, rebooted, and registered again with the Target Group. Those Target Groups have redundant targets - so the missing one target is okay for the time it takes to make it become functional again.

So now my actual question. Can this easily be automated or is there some light-weighted solution available? If possible I would like to avoid a "full-blown" fleet management software. However, I can see how it can get complicated fast but still thought to ask.

My first thought was some sort of AWS-CLI scripting that unregisters the instance from the target-group and registers itself again after the reboot succeeded. If there are enough other targets available to cover for a few minutes. Or maybe have the instance shut down and let an auto-scaling group boot up a new instance. However, that new instance would need to be updated from the base-image first as well then.

Any idea where or what to look for?

Thanks, M