It seems that I must have bought a twin sister of your setup, but I bought it 5 years ago and it is still in the box. I am going to install it, beleive it or not! I did some bench (radio shop) testing of the RC-40 (0-->4000rpm) Sun meter. It had 114.2 ohms internal resistance, 0.072 Vdc across the movement, and more importantly, it drew 0.000630 Amp for full scale deflection. So when it is drawing less than 1 milliamp of current at 4000 RPM, a AA battery is going to last a long time. For more useless information, the original RM12R Mercury battery was rated for 1.35 Vdc vrs the 1.5 Vdc for a alkaline AA battery.
Since I own about 20 different old tube-type Heathkit radio test units, I also have a Heathkit MI-31A tachometer, which is transistorized, but is switchable from 8k to 4k RPM, 6 or 12 volt, AND positive or negative ground! I am going to install it in my 1941 Packard 6, when it becomes roadworthy.