I'm going to suggest you clean both battery terminals well for starters.
Then follow your negative cable to where it grounds, and remove and clean
the cable ground. Next, find and clean both ends of your engine ground
strap (you usually find it on the back of the engine connecting to the
firewall).

Since you removed the alternator, I assume the battery connector on the
alternator is clean and tight as well as the other connections.

Not sure that will fix it, but it eliminates this as a cause, and is simple
to do.

If that doesn't fix it, post back and tell us how fast it cycles the
voltage up and down, and whether that cycle stays constant as you rev the
engine.

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