While a little variation in alternator output with engine speed is normal, so (unfortunately) is gage inaccuracy in the voltmeter. The first thing to do is verify alternator output at the battery terminals with a known accurate voltmeter (viz. a DVM.) If that's good, you can quit worrying about it, and just keep an eye on things.
If not, here are a few things you can try. Fortunately, the 89 uses a Delco internally-regulated alternator - ChryCo got the brilliant idea later to use a regulator in the PCM - if it gets cooked, the only fix is to replace the PCM, or use a "one-wire" alternator.
Before you do anything else, visually check all connections where you see a large-gage wire, and clean as necessary. Recheck if you clean anything.
Start at the battery with the engine OFF - check voltage and note it (seriously, WRITE IT DOWN! You'll forget if you don't...) This is your baseline. Leave the DVM negative lead clipped to the battery negative terminal for the rest of these tests.
Check voltage at the large screw post on the start relay, since this is the main distribution post for the rest of the system. This should be within two-tenths of a volt or so of battery voltage. Repair if not.
Check voltage from at the alternator output post (on the back of the case.) This should be within two-tenths of the reading you got at the start relay post. Repair if not.
Switch your DVM to the "continuity" beeper if you have one - or a low ohm scale if not. YOu'll still be working from the battery - terminal for these.
Check resistance from the battery "-" post to the other end of the ground cable at the engine block. Should be 0 - or really close to it. Repair if not.
Check resistance at the alternator case - should also be about zero. Typical repair for this is an "alternator bonding cable" from the threaded boss on the back of the case to teh battery "-" terminal.
Recheck all voltages with the engine running, and see if full alternator output is making it to the battery and the start relay post. If the voltages are good going out, they should be good going in, but check anyhow.
It might be worth taking a jumper cable from the alternator mounting to the battery - post and seeing if that changes the output. Sometimes the alternator case does not ground well through the mounting, and that is where the case bonding cable comes in.
Feel free to repost, email, or PM if I/we can help you some more!
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