With this, and your other Post ? Not being able to hear the actual "Beep".. it's real hard to offer any solid trouble shooting hints.. other than:
Does this truck have a Battery Minder/Trickle Charger on it ? (the beep being a Low Battery alarm) (beeps until the batts go Flat/Dead.. in 2 minutes)
How old are the Battery's ? (old worn out batts could have fried the Alternator)
And.. If your not getting 14.?, but not more than 15 volts, at the Batts, when running.. with 200+ K on an OEM (if it is) Alternator.. you might just go ahead and replace the Alternator.. and see what that does for the "Beep" ?? BUT LOAD TEST BOTH BATTERYS FIRST.
Joe
Is this 89 New To You ? or owned by you since new ?