I tend to agree with Vic as in many simple systems the current for the light actually goes through the brushes. However for the cost of replacement brushes (with regulator) it may be worth doing just to see. This is assuming your alternator has a popular car type origin.

if it is as I am familiar the regulator is a little black plastic block about 20mm across on the back of the alternator (opposite end to the pulley) with 2 screws holding it in. It has wire push on connections or a plug. When you remove it you will also remove the brushes and be able to see the slip rings. (hopefully) the rings should be clean and bright not too burnt.
It is worth having a check olewill