It should come on with a COLD engine start and run for about 45 seconds to one minute.
It's purpose is to heat up the catalytic converters quickly so we can hug more trees.

The blower is simply that : unintelligent and purely controlled by the RCM relay via the PTCM.
I'd guess there is a 99 percent probability that the relay contacts are burnt / sticking.

( the big orange fuse on the RCM is for the blower )