Looking for a PCB flag/indicator component
There are non-volatile electromagnetic indicators that can be used. 



They are a little oddball though. They were originally developed by the Canadian unit of Ferranti-Packard, but the patent has long since run out. 

They work like a bistable relay (electromagnetic) and retain their state with power off. In the old days they were used in quantity for airline status displays in airports. 

Personally I would consider fitting the trays with batteries (or applying power later) and using LEDs. You could store the information in a non-volatile memory such as a small microcontroller with on-board EEPROM or FRAM if the power has to be interrupted.