Ahh, THAT explains why so many pilots struggle with their first jet. It is so long ago I can't remember what my instructors taught, but as they were ex military, I suspect that they said it a little different. I do remember one of them saying that pitch only controlled speed when there was no power, as in a glide approach.
Davies in his bible " Handling the big jets" says that the throttle is the speed control and pitch is the flight path control.
It even works on bugsmashers, so I don't know why it is not taught that way from the start. It would save having to realign one's thinking later.
The basic autopilot is a dumb animal, and certainly if in IAS mode it will vary pitch to hold speed while the rate of climb or descent will be a function of power.
When VS mode is used (if your autopilot is post Stone Ageand actually has this mode) it reverts to power as speed control. This is the mode I prefer for descent in a non autothrottle aircraft as it forces one to keep a hand on the throttles for speed control. But there are so many ways to skin a cat that I am not saying this is the only way to use older tech autopilots.
As someone else has pointed out, with these older autopilots, use of VS in climb is a no no, because the demanded rate of climb could exceed the aircraft's performance capability, with resultant stall.