With a 12V conversion you should expect half the normal current reading as the 6V. If you add electrical accessories such as AC clutch and blower fans or - Lord save us - electric heaters, you should bypass the ammeter with properly sized wire.
An ammeter should not overheat within its dial range. If it does, the cause is faulty connections either internal or external. Wire terminals should be soldered for best connection. Those hardware store crimpers really don't do it.
I believe the current is the same, 6 or 12v.
When converting from 6 to 12, all the loads (coil, starter, lamps, wipers, etc.) have to be updated with 12 V components, or a Series limiting resistor installed on the 6V part.
Essentially; the 12v replacement has twice the resistance of the 6v part, or the series limiting resistor is sized the same as the 6V part and when put in line with the 6V part doubles the resistance of the 6V part for 12 v operation. Eitherway, way current is same: 6V part on 6V, 6v part with series limiting resistor on 12 V, or a 12 volt part on 12V.
An ammeter shunt is only needed when using alternators. They can deliver a max of current of 80-90 amps, ******* a 20 or 30 amp max ammeter. High readings can happen if the alternator is not regulated. Case of high output - short time after starting until the battery refreshes from starting. Longer high output - a partially discharged or bad battery, Halogen lights, lots of optional lights (cowl, fog, etch), air conditioning, etc. A properly shunted ammeter halves the current going through it, and you have to double the reading in your head to get a true reading.
For a long time I had difficulty getting my head around all this, info was spread out and I am not as quick as I once was learning/understanding all this new to me info.