gasket, such as it is, very thin, 1/4 inch rubber, flimsy, and insubstantial, along the very top of the windshield glass

The gasket runs along a very shallow channel, "separating" the top edge of the windshield glass from the actual forward edge of the roof.

It is not sitting in its tiny channel, except at the ends on both sides, hanging down on the windshield for about 1/2 inch.

This does not seem right. It seems to me that the windshield glass should be better protected.

Should I apply some sort of gasket cement along its very shallow channel?

Thanks for all replies!