2006 Prius electrical issue

I am having an electrical anomaly that is increasing in frequency. It acts as if there is a bad connection to the aux battery.

Occasionally, when I get in to start the car, it seems as if the aux battery is disconnected: no dome light, no indications on the instrument cluster, no response to the power button and the rear hatch must be opened manually. Usually, the dome light comes on when wiggling something on or near the battery. Sometimes it comes on while wiggling the negative battery terminal, sometimes the positive, sometimes one or the other connectors on top of the battery. And then sometimes, it comes on when opening or closing one of the doors or when trying to crawl through the trunk to manually release the hatch.

The other symptom, however, makes me think there may be more to this than simply an intermittent connection. Occasionally, when turning the car off, it goes off briefly (less than a second) and then comes back on. Other times, it will go off, I can get out and walk away with it off. But when I come back later, the car is on (not running but on).

I have become very intentional about how I press the power button and noting that the car is truly off and stays off, so it is not a matter of quickly or incompletely pushing the button.

I am beginning to wonder if there is a bad relay or something other than just an intermittent connection.

Any thoughts on what would would cause it to not only lose connection but also power on randomly? Any suggestions on what to look at?

Thanks

 

BTW, I meant to add that I have removed the connections from both battery terminals and cleaned the terminals and connectors for both (even though there were no visible signs of corrosion or debris).