Wire gage size?

The big problem with the bulkhead is not the gauge sender wires, but rather the high current connections. I would run AT LEAST no8 through there, depending on how large your alternator is. Consider getting rid of the ammeter. Yeah, I know. I grew up "an ammeter man" myself.

Read this:

http://www.madelectrical.com/electricaltech/amp-gauges.shtml

from here:

http://www.madelectrical.com/electrical-tech.shtml

Drilling out and upgrading wire size through the bulkhead is one way

Usually you can pull the bulkhead apart and SEE the problem with "meltage" to the plastic, obvious that the connectors have got hot.