Many Possibilities at this point
It certainly could be a current drop, do you have an ammeter to watch that? Depending where an ammeter sits you can make conclusions about whether the battery is participating in the problem, or if the regulator is suspect. Determining if it is the alternator itself can be done on a bench check at your local car parts supply.
It could be a voltage drop by resistance either on the field side or supply side (yikes) including grounds.
Start checking voltages in different places, then start isolating variables with some known good values.