Yes, it is possible the 6v gauge could be damaged if a Runtz-style 12v-6v reducer is not used.

However, a few members have posted that they have not used a reducer when switching to 12v, and they have had no problems. I did-not/do-not gamble - I have (for many years) used the reducer from Classic Parts.

I do not know a way to determine 6v or 12 gauge.

I'd buy the gauge first; and, if that does not solve the problem, then buy the sending unit?