Prevent Deadlocks in Vendor Databases
As you are on SQL Server 2014, you can simply harvest historical deadlocks from the system_health Extended Events (XE) session and do some analysis.  It should be running all the time and will contain deadlocks since that last SQL Server service restart, although the ring_buffer could have cycled and ejected some older records.  Try code from here or here.  This 
No need for Trace flag 1222 and no need to run Profiler / server side trace with the Deadlock Graph event which can only capture deadlocks from the time you start them / turn the trace flag on.  You can just look back in time.

As the WSUS database is relatively public domain (and not your secret business logic database) you could publish some of the deadlock XML here and we can help with the investigation.  Deadlocks are sometimes due to missing indexes, or if there are excessive exchange events then might be down to parallelism.  Let's have a look!