The only difference between an Alpine tach and the Tiger one, is that the face is different (7k and 5.5k ranges), and the Tiger one will receive twice as many ignition pulses per engine revolution as the Alpine one. The net effect is that the Tiger tach needs less amplification of the ignition pulses to produce the correct reading, and the amounts for each are generally within the range of adjustment.
The bigger problem with the old tachs is that the capacitors crack or otherwise become 'leaky', and the old germanium transistors are not really good for the job - you could probably sell them to a music enthusiast to make a distortion pedal and pay for the rest of the tach rebuild with the money you got.
I have been building tach circuit replacement boards for over 20 years, most specifically to deal with issues that occur when people use pertronix or other points-replacement systems. If you're not ready to dive into the tach and start replacing parts then that board might work for you... I supply them to Tom Hall as well as doing tachs for people myself and we have done several hundred over the years.
The OEM instrument voltage stabilizer is a bimetal contact strip that is dependent on heating effect of a wire wound around the strip and by the amount of current going through it. The first important thing is that it must be mounted to an electrically grounded surface. Secondly, it may require the gauges to be connected to provide a nominal load. Then, the output of the "stabilizer" is a square wave that switches between 0 volts and whatever the input voltage is, presumably at a rate that reduces the average voltage to 10 volts. These things generally work OK for a while and then the points get dirty after a number of years, and they stop working consistently.