Update 3/8/19:
1. I ran the Chrysler drive cycle for the O2 Sensor Heater Monitor exactly as written in the document linked by
@mrblaine in Post # 18, specifically: start with a cold engine, idle five minutes and remove key, wait 10 minutes before checking the O2 sensor heater readiness monitor. No joy.
2. I experimented with a modified Chrysler drive cycle for the O2 Sensor Heater Monitor by leaving the jeep in the garage for 48 hours to let the engine and all fluids stabilize at ambient temperature, chocking the wheels and then idling in Park for 5 minutes, idling in Drive for 5 minutes and idling in Neutral for 5 minutes (total 15 minutes of idling), then shutting off the engine, removing the key, and letting the jeep sit for 48 hours to thoroughly cool down before checking the readiness monitor. Still no joy.
3. Having concluded from multiple tries at the Chrysler drive cycle, several weeks and hundreds of miles of driving, that there is a design anomaly and the O2 Sensor Heater Monitor in 05-06 Wranglers will never show ready for emissions testing unless the work detailed in TSB # 25-005-13 is performed under Chrysler's extended emissions equipment warranty, I decided to see what would happen if my smog test guy hooked up my jeep to the California emissions testing system and ran the test even though my O2 Sensor Heater Monitor showed not ready -
My jeep passed emissions testing instantly with no further muss or fuss.
Conclusions from my research, experimentation and personal experience:
The California Bureau of Automotive Repair is aware of a design anomaly in all 2005 and 2006 Jeep Wranglers that causes the O2 sensor, O2 sensor heater and Catalyst readiness monitors to show not ready for emissions testing even when they are. [California BAR Smog Test OBD Reference, 10/12/18, page 22]
Chrysler has issued TSB # 25-005-13 (rev. 9/12/13) which is a workaround for this design anomaly that consists of one or more jumper wires and a few splices in the vehicle Power Distribution Center (PDC).
Chrysler has confirmed an extended emissions warranty for 2005 and 2006 Wranglers with this OBD readiness monitor issue, without expiration date or mileage limitation, for the parts and labor in connection with TSB # 25-005-13.
TSB # 25-005-13 will need to be performed if there are issues with the O2 sensor or Catalyst readiness monitors before an '05 or '06 Wrangler can pass smog in California.
TSB # 25-005-13 does
not need to be performed for emissions testing in California if the
only issue is with the O2 sensor heater monitor.
Assuming that there are no other issues, 2005 and 2006 Jeep Wranglers showing the O2 sensor heater monitor as "incomplete" or not ready for emissions testing can and will pass smog because the check digits in the VIN automatically alert the California emissions testing system to the exemption for the O2 sensor heater monitor.
Since I am experiencing no issues with my O2 sensor and Catalyst readiness monitors, and am able to pass smog in California even though my O2 sensor heater monitor shows not ready, I have elected not to have TSB # 25-005-13 performed at this time. It doesn't matter to me that the check engine light won't flash multiple times each time I turn on the ignition to alert me that the readiness monitors work properly - I have an OBDII scan tool for that and would prefer not to resort to a wiring hack unless absolutely necessary.
And that concludes this chapter of "Unable to Pass Emissions." Thanks to
@mrblaine,
@L J and
@TJDon for the valuable pieces of the puzzle that each of you posted.
But wait, this chapter may not be over.
@OldButStillJeeping, did your jeep pass emissions at an English speaking smog test center with your incomplete O2 sensor heater readiness monitor?