Scheduled EventBridge rule targeting API Destination

Is it possible to create an EventBrisge rule which can be scheduled to run at a certain time of day and call an API as a custom target?

It seems as though a schedule can be setup for targets if they are AWS or Partner services, but not if they are custom configured endpoints.

All I want to do is setup a daily routine to call an endpoint so it can perform a daily cleanup task. If there is a better way, can someone suggest it, please?

EDIT

Under EventBridge I have created a Connection which points at the OAuth endpoint and then an API Destination which points at the API endpoint I want to invoke on a daily basis.

I have then created an event bus and a rule but when I try to set the Schedule option on the rule it shows a warning which states:

Schedule rule is not supported when custom or partner event bus is selected

I believe this means that I cannot invoke my own API endpoint with EventBridge without going through a Lambda. Am I wrong?

Create your scheduled rule on the *default bus* using the Create Rule interface. It appears you are right that the brand-new EventBridge Scheduler console interface does not yet (?) support API Destinations.

The "create rule" scheduling supports cron-type use cases like yours. EventBridge Scheduler adds new functionality like ad-hoc scheduling of one-off events, flexible time windows, and TZ-aware scheduling.