Yes, it should buzz for two to five seconds and stop. But it doesn't
stop, it just keeps buzzing. The battery is new and is testing fine.
I changed the fuel pump relay and the EEC relay and neither made a
difference. I think the relay under the dash you are talking about is
the EEC. Its not the ignition module because it acts the same whether
that is hooked up or not. The alternator is testing fine so the voltage
regulator should be good (VR is on the Alt). And I know the tach is
not supposed to move, but it does. I am not sure what else it could be
and I dont want to start buying things to troubleshoot it. I was
hoping someone on here would maybe have experienced something similar
but everything that is wrong seems so wacky.

Thanks for your help.