To Michael Harrington,
The bulb wire contacts are corroded to the socket contacts. Protect your fingers/eyes as the glass bulb will likely break.
To extract the fragments of the base, I used my scratch awl from atop as well as from the sides of the plastic socket. There is a hole on either side thru which
the awl can be inserted, then pry the tip upward, pushing the glass fragments up and out.
Clean the oxidation waste, apply dielectric grease liberally on the contact points.
These units are not moisture tight hence the corrosion. Using rope caulk may improve the seal.
The caulk can be easily removed at the next bulb replacement.