73 Dart Alternator doesn't show charge anymore.

Took out the bulbs for the grille parking/indicator lamps, as they were the only bulbs I haven't replaced recently, and they've definitely seen better days, can bad sockets like this cause short? I didn't seen any continuity between the bulb and the socket on my multimeter.

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A bad socket will result in poor grounding.
An incorrectly installed double filament bayonet base can result in some weird cross circuit shorting