tach/rpm problem

I have a 90 lumina euro 3.1, for about a year the tach shows a higher than normal rpm's. Just in normal driving range around 65 it stays between 4 and 5, then if I give it alot of gas the tach goes really high before it shifts, sometimes in the red. When I shut it off the tach stops around 2. Recently, I had to unhook the battery for other things I did & it's died a couple of times. Then when it dies the tach goes to 0 but when I shut it off it stays around 2. It runs pretty good, but not as much power as a few years ago, but it has 180,000 miles on it. Any suggestions would be greatly appreciated. NO Codes either.

first guess would be that the signal the tach is getting is too hot for some reason. Perhaps where your tach ties into the coil pack? Electrics are a bear to track down.

Thanks for your reply. We will try that route.