Shower light blinks immediately after vent fan is turned off
First, "until the fan stops spinning" is straightforward enough — a simple AC motor that is spinning but without power applied will act as a generator, supplying the electricity that the switched supply isn't any more. The higher efficiency of LED lighting — and the electronic LED driver circuits used — mean that they can run from lower voltages where an incandescent bulb would be too dim to see.

If your light and fan were on the same switch, this would be enough to explain things. But you imply they aren't because you say the light turns on rather than that it was already on.

There must be something electrically weird going on beyond what I've described so far, to completely explain things. I would suggest updating your question with photos of the interior of the fan and the light pulled apart, and if you have any type of “smart” switch rather than a simple toggle, give the details of that.