Plenty of bells ring with this type of issue, but let me ask; are you cycling the power before you call for service (for the benefit of your tenants), or is the service tech approaching a non running unit? This plays a big part.
The fact that it sits overnight and this inactivity triggers the problem may be a good clue.
Also, can you determine, when you arrive in the mornings what floor the elevator is on? Either a position indicator in the hallway or you can peek through the doors with a flashlight if they open from the center or from the side gap between the door panel and the door jamb to determine its location.
Any clue especially repetitive ones help the tech to narrow down the possibilities.
Service maintenance contracts aren’t cheap, but it sounds as if you either don’t have one or it’s the rock bottom contract which does not cover callbacks nor parts.
