Had the same on my s16 this time last year.
Had the old alternator rebuilt by a local company, then shortly afterwards the rest of the car died.

Have an s16 alternator, done less than 500miles that i want to sell £40 deliverd.

ok, well, after some swearing.... I've completed the job, swapped the alternator out, and thankfully, it now works properly. :

Total time taken was about 6 hours, which was fun in the snow yesterday, and frost first thing this morning... not

I've also managed to crack both breather pipes when refitting this morning.. they had gone brittle in the cold, and fractured when refitting to the top fitting. Doh !

I've bodged them together with some electrical tape that will hopefully be ok until I can get replacements..

Car seems to be running fine, and no new leaks etc.. Battery light now goes out, and the voltage at the battery is over 14v when running.

Just in case anyone should stumble on this thread when looking to do the job themselves, heres a few hints, that could save you some hours !

I followed this
(Replacing inlet manifold gasket)

for how to get most bits apart, and to get at the alternator itself.

There are also loads of electrical connectors and one or two hoses to remove before you can get the manifold off, that arent mentioned, so allow plenty of time

The two bolts holding the alternator in are a PITA to get at, easisest way seems to be via the driver side wheel arch.

This FAQ,
(Changing AUX Belt FAQ)

is very useful, if you take the belt auto tensioner off, ( and pre-tension it first ! ), then getting at the bottom bolt is easy, and the upper is just a fiddle..

Putting it back together, it seems to be easier to put the top bolt in first, then the bottom.

Can't remember anything else immeditely, its actually a fairly simple job, but took much longer than I expected, not least because until you remove the autotension belt, getting at the alternator bolts is so hard !

Thanks to the guys who wrote the various FAQs, they were really helpful :