Well, I am posting this as a question, hopefully some of you fine folks
can help me figure out this problem I have been having. I thank you
ahead of time for you replies.

I have an 89 Accord, roughly 145,000 miles. I have owned the car about
a month. The problem starts there, I have regularly had to pour gas
directly into the carburetor in order for it to start. This was very
strange, because after about 4-5 times, the car would finally start and
run. So, I thought maybe it had something to do with the choke heater
or electric choke actuatoror maybe the fuel pump was weakening.

Then, on a recent long trip, the alternator light came on. It did not
appear all the time, only intermittently, and when it would come on, I
could depress the clutch pedal and rev the engine up over 3500 rpm and
the light would go out. Eventually, it acted as though it was starved
for fuel, like the fuel pump was going out.

I removed my alternator (oh, what fun!) and took it to be tested at
both Autozone and O'Reillys. Both tests indicated the alternator was
good. I re-installed the alternator, and then took the battery to be
tested. It also tested good. I was ready to pull my hair out!

I got on here to read about other who might have had the same problem,
and I checked the Haynes Manual for my car, and basically I am at a
loss. If the battery and alternator are good, then why would the light
come on?

I noticed the alternator and the fuel pump are on the same fuse. So,
today, I installed a new fuel pump. It no longer acts as if it is
starved for fuel, but the battery light now comes on again. Again the
light will go out above 3500 rpm, but comes back on as the engine
returns to idle. Can someone please help diagnose this ghostly problem?