Even if you knew what voltage the coil was designed for you would still need to know what size resistor was engineered to go with it (unless it is one of the later coils with an internal resistor built into it, which I doubt this one is) Excessive current is what melts the very fine windings in the coil. A separate resistor is installed in the circuit to reduce the current flow in the primary windings. If you run a coil without the proper resistor it will burnout in a very short time. I have seen them do it in a couple of days.
The insulation between the windings of old coils goes bad. For that reason alone I would buy a new coil along with the resistor that was engineered to go with it. If the coil is for a restoration or some rare vintage racing coil you can have them rebuilt, with modern insulation materials they will be better than new. We also don't know if this coil was designed for a positive or negative grounded system, it does make a difference.
I still did not answer your question. Could you measure the resistance of the coil and figure out what voltage it was designed for? I don't think so, not without knowing the value of the resistor that went with the coil. You could possibly power it up and measure the amperage draw and figure it out that way.
I’ll give you an example of what I’m talking about. Most older coils (12 volts) need about 5 amps of current in the primary windings to multiply the voltage in the secondary windings to produce the 20,000 to 30,000 volts it takes to jump the rotor gap and spark plug gap. The primary winding resistance plus the value of the separate ignition resistor divided into the battery voltage will give us the amperage draw of the primary circuit. Not enough amperage and our spark will be too weak, too much amperage and the primary windings will melt. The primary windings are made from very fine wire that is like a human hair, it might run for decades on 5 amps but burn like a fuse on 10 amps.
I dug out an old ‘66 Mustang Shop manual to get the specs to show you how Ohm's law works.
Primary winding Resistance 1.40 to 1.54 Ohms at 75 degrees
Primary Circuit separate Resistor 1.30 to 1.40 Ohms at 75 degrees
Amperage draw engine stopped (points closed) 4.5 Amps
Amperage Draw Idling (points opening and closing ) 2.5 Amps
Ohms law says if we divide the resistance into the voltage we will get the amperage (current flow) of the circuit. 1.40+1.30=2.70 Ohms. 12.6 volts divided by the 2.70 Ohms of resistance gives us 4.66 amps of current. Ford and most manufacturers had a ignition resistor bypass circuit which boosted the coil output voltage during cranking to help ignite the fuel mixture, it’s like throwing a little extra lighter fluid on the barbecue to get it going. In this bypass mode they do not use the external resistor, the 12 volts goes directly to the coil. In this cranking mode we only have 1.40 ohms of resistance in the primary windings. When divided into the 12.6 battery volts it gives us 9 amps of current. This in theory should double the intensity of the spark. This is ok for cranking an engine for 15 seconds but would burn up the fine windings if driven for any length of time.
If we took that same 12 volt coil and ran it on 6 volts what would happen? Lets do the math, 6 volts divided by 2.70 Ohms would give us 2.22 amps of current. That is not enough current to produce a large enough magnetic field in the primary windings which boosts the voltage in the secondary windings. The car might start but would probably crap out at higher engine speeds. If we eliminate the external resistor we would have 1.40 Ohms divided into 6 volts which gives us 4.29 amps. The 12 Volt coil would probably work ok on a 6 volt system if you eliminated the resistor.
Stick the coil on the shelf for garage art and go buy a new one.