Voltage drop when engine under load

04 Sterling with Cat C-12. For the last week or so my voltage just been all over the place, no starting or dead battery issues. Replaced the alternator and no real change. It will sit at high idle (900 rpm) at 13.5V but when the engine is placed under a load it starts to drop to as low as 12.4 V depending on how hard the engine is working. When I get over an incline and roll downhill with the engine being able to "relax" the voltage immediately starts climbing to above 13 V, but it drops back down as soon as it's pulling again.
Also after startup I need to rev up the engine (never had to do this) to get it to start charging.
This afternoon I replace the batteries and jump cables but as far as I can tell on the yard it's still doing the same thing. Any thoughts ? Thanks

 

Interesting, I'll definitely try that. Thanks.

 

Never fixed it. I monitored the voltage with and independent meter from the cigarette lighter, which was normal. Also the truck ran fine and since was sold.