It should or may or if it doesnt you know where to look...
Biggest issue on older incandescent bulb holders is the socket to mount joint comes loose or corrodes between (mine steel sockets were rusting). Its simply swedged on to a bracket.
That's riveted to al. backing plate that is grounded by lead that crimped to copper wire that is riveted, ....These are Bargman fixtures, aluminum plates and rivets subject to corrosion. Mine the lead riveted between plate and the connecting bar you could spin.
Following the fix of others I ended up running a jumper wires from the ground lead. Cut off the crimped on connector and added 2 wires soldering directly to base of bulb receptacles. Left original ground path intact. Not sure why some aftermarket mfgs don't hard-wire ground.