That's what was up with my lunched shifter that I bought. I used it like that for a while until the other trigger started to jam as well. I lost patience in the end.
I wish I'd tested it before I did (I bought it at Christmas, but didn't get the bike up and running until then so it was too late to try and get a refund etc).
2015 Stanton Ti Switchback
2006 Specialized Demo 8
2013 Specialized Allez Sport
1999 Santa Cruz Chameleon
1994 Cannnondale Beast of the East (rebuild still in progress)