I have a 2004 X type 2.5 and the codes are reading P1647 and P1646. I
believe these are both upstream O2 sensors. A mechanic friend told
me that you could take them out and clean them with carb cleaner and
a toothbrush and it might fix them. Does this sound like this might help
if the aren't shorted out?

 

no

 

RonnieJoe: The upstream sensors have an electric heating element that burns out with age, like an incandescent light bulb. Your mechanic friend is well intended, for sure, but once the heating element is toast (pardon the pun), it's time to replace it.

I'm thrifty (full disclosure: my wife says "cheap"), but replacing the upstream O2 sensors saves on your gas bill and protects your catalytic converts, which are far more expensive, and far more effort to replace than O2 sensors.

Here's an eBay link for $75 sensors:
New Bosch Airfuel Oxygen Sensor 15627 for Jaguar 1999 2008 | eBay