I'd suggest the following test in the test environment
1. Have a lock monitoring script running as a job on the server, the monitoring script only monitors the locks on table master..T_DBA_ConnectionTracker, and it should be run continuously against sys.dm_tran_locks (mainly look for X locks, BOL has several good examples.) and recording these X locks to another table / or simply send out the email.
2. From several other clients, try to log on to the server with the original logon trigger turned on
3. you can coordinate step 1 and 2 like this (for example): step 1 runs at 10:00am, step 2 runs at 10:01am
If failure occurs on 2, we can check what have been logged in step 1.
Another approach is in your original trigger, put a try... catch block and if there is an error occurs, just log the locks on master..T_DBA_ConnectionTracker, (However, I have not done this, i.e. whether I can put a try..catch block inside logon trigger, I will do some tests on my side as well and post back if I have time).