Very odd. When my blower failed it would run a few seconds and
then stop (the lights then came on). I think the controlling
computer detected the fan was drawing too much current and shut
it down after a couple seconds. This would repeat every time the
car was started.

There are also some issues with a relay that controls the blower.
I've never dealt with it. Hopefully, someone else will mention
how to look at that as a possibility.