If you are pressing the switch directly and it fails to read the most likely cause is mechanical failure and a new switch will need to be soldered or swapped put I honestly forget I'd the left and right triggers on the steam controllers are modular or soldered driectly to the boars. But once the contact plates inside a switch wear out there isn't much you can do.
I'd try some isopropyl alcohol, de-oxit or bw-100 to see if the trigger starts working magically after being cleaned out property