My 6+ year-old water heater's pilot light won't stay lit. I held down
the pilot light switch upwards of 5 minutes and it still extinguishes
when I let go. The flame encompasses the last 2-3 mm of the
thermocouple so it's positioned correctly. I put in a new
thermocouple and same problem.

How likely is it that the new thermocouple is bad?

How likely is it that the control unit is bad? If the control unit is
bad, should I just replace it or replace the whole water heater?

Thanks!

Getting cold in Austin ...