I once replaced a diode in a Bosch alternator. In the alternaters I have looked into there are three large diodes that convert the main current into DC but then there are three smaller that convert the current that goes through regulator and "pre"-"magnetizes" the rotor, if I remember right.

Thought it was one of the large diodes, but in fact was one of the smaller that was broken. Symptoms were same as yours. So, if you are going to try this, start checking the smaller ones, if your alternater is similar inside. Be careful using a small soldering tool when de-soldering, and try holding (if there is room for it) with a plier to dissipate heat, applying it between diode and soldering point (all electronics stuff very heat sensitive;this is reason why not suggesting undoing all before testing them, one culprit is enough to cause your problems).

You have to disconnect each diode at one end to be able to check it individually, to find which one is bust. This is simple. Then you need to read the little text on the diode, and find a similar one. This can be really difficult (I had to go to a major manufacturers main distribution central, and donate some money to the coffee money box (2$). But to get to the point of finding the diode that is bust is not more than an hour of work.