I drive a 1993 BMW 318i, and I was just wondering at what point it would be best to shift gears. If you could provide answers for both maximum performance and maximum fuel efficiency, I would appreciate it.
The ideal times will often be buried in the car’s manual somewhere.
Max performance is easy…red line! (or just a little past).
Max economy is probably 2K. Remember, we’re talking max economy here.
The trade off is probably around 3k where most people change gears. I normally kick it up +2K above that for passing and do a red-line drop for extreme changes in speed.
I usually just listen for the engine revving.
I’ve been going by the engine revving too, and I’m sure that I’m doing a pretty decent job of it. I was just wondering as to where the ideal shift points would be.
In a car with over 50k miles, which I’m assuming yours has, you won’t be able to find the optimal shift point with anything except your ears. Like speedometers, tachs lose calibration with engine running time, and the older they are, generally, the larger the delay between engine revs and shown revs.
When the clutch is disengaged, obviously. 
Mind my words, someone will come along and argue with that…