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Is the tach at 25 all of the time or just when you shut off the car? My tach pops back up to 25 when I shut off the vette but works fine otherwise. I've heard of a lot of other vettes doing the same, I think it has something to do with the HEI and voltage remaining after the key is turned off but I can't be certain. Anyway, cool vette, I'm slightly partial to 79's too, but maybe that's because I have one. And yes, that is an 80-82 rear bumper on yours, the spoiler for the 78-79 was a bolt on spoiler, sort of an afterthought, rather than blended as the 80-82 was. Welcome to the vette community.
You should have an electronic tach. I have no experience or knowledge on exactly how the tach works so I cannot give any advice except for you to post a question about it and I'm sure you'll get plenty of suggestions.
As far as the 'wave' in the spoiler, that's typical of those spoilers. I think the only way to avoid the wave and discoloration is to get a fiberglass replacement bumper, but if it's not a show car (or you're going for NCRS) then the wave is no problem.