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If you paint it, do it like the factory did, not totally painted body color like the top side.
I am working on a 71 B-body and it is a factory undercoated car. We did it with dip primer and overspray like the factory. Took pics and then undercoated the undercarriage like it was according to the original pics we took. I like the results. Just be sure and use the correct undercoating and you will never have any problems cleaning it after it dries.
If it were my car and I was doing it as close to original as possible no doubt it would be undercoated, especially since it was a FACTORY undercoated car and not done by the dealer.




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There's always another option as well. Follow the above procedure and stop before adding the final undercoating, or just do the wheel wells like all cars got. You can always add the undercoating later on if you so desire. Don't forget, undercoating cars also got under hood pads. If you decide to leave off the undercoating, also leave off the under hood pad, again, it can always be added later but the clips will usually scratch your paint going in so be sure before adding one.