Based on this report, I believe the client identifier is being set correctly, and it's time to enable both tracing and statistics collection.

This code snippet turns on tracing, statistics collection, and sleeps for my specified data collection interval of 60 seconds. Since I am using only the client identifier to screen sessions of interest, I enabled statistics collection using the client_id_stat_enable procedure. I want the trace files to include both wait event details and bind variables (which you can lose when consolidating trace files) based on the client identifier. Therefore, I enabled tracing using the client_id_trace_enable procedure.

This report shows the activity during the collection interval only for the sessions of interest. Also note the use of the v$client_stats view, since we were collecting data based on the client identifier. We are provided with different types of statistics: DB CPU (service time), wait times (queue time) related to IO and RAC, workload statistics like db block changes, execute count, and user calls. This is a wonderful collection of statistics that can be used for firefighting, response-time analysis, and predictive analysis.