Originally Posted by Frenchiejo
it is showing 13 at the battery
I would accept that voltage as good, your converter is charging and the batteries are more than likely in good shape.
Back to your concern about lights going dim - sometimes when a converter changes its charging stage (bulk at 14.4V, absorption at 13.6V and float at 13.2V) the 12V lights can faintly change luminescence (i.e. brightness) due to voltage going from 14.4V to 13.6 to 13.2 V. Not normally noticeable unless you are really looking for it....
If you still have concerns, measure the voltage on your batteries when the "lights go dim". If you still have greater than 13V I would say that is normal.
If it is just one light going dim, the bulb may be ready to blow, or there may be a problem with that one light circuit. My thoughts.
Hope this helps,