First, when you say HEI, do you mean the GM Big Cap HEI? Reason I ask is because guys commonly refer to anything that isn't points, ie, electronic ignition as HEI. If it is the GM big cap HEI, the cap has a tach terminal, and there is a really good chance that it will work just fine, maybe not be the most accurate, but it will work.
Aftermarket tachs commonly have a power, ground, signal and lighting connection. That isn't true of the OEM tachometers. They were commonly grounded to the dash, had one signal wire, and a plug in lighting connection.
If it was me, I would not worry one bit about burning anything out. If you are, just use a small inline fuse when you hook things up to any power. Looking at the back of the tach, that blue wire looks like the plug in light bulb. That, I would tee into the illumination circuit off the headlight switch. You could even tee it to something like an ash tray light or radio illumination circuit.
One of the other wires is a signal wire. What I would do is ground the case, then try hooking one of the other wires up to the tachometer terminal and look for function of the tachometer.
Here is the tachometer section of the 1966 Chassis manual, not much help, but it looks like that red wire to the center terminal is the signal wire.