Answer:
It can be either the progressive stem of the verb, or the gerund, which makes it a noun form. It can also be used as an adjective.
E.g. "The star was glistening on the Christmas tree" is a verb form, the progressive stem.
But "There is some glistening here which I would like to investigate", is a gerundive noun form.
And "Her lips were covered in glistening lip gloss" is an adjective form.