Hey Tazza-
The electrical part of the system is of course practically instantaneous.
The coils on the valve operate pilot valves on either side of the aux control spool. The spool is centered by a springs. If the springs are weak, it may be slow to stop moving.
If it is slow to start and stop, you may have a pressure problem. The aux pilot pressure is the charge pressure, controlled by relief in the hydrostatic pump. It may be low, just in the range to keep from producing a code or lighting a warning lamp, but slow down your aux. Low pressure can be from a bad pump and/or relief poppet. This is more likely the problem if it acts okay at high rpm, but performs increasingly poorly as you back off on the throttle.
But with the age of the machine and in my experience, it may be one or both aux valve stems, or the guts under the aux coils on the valve. They have little screens on them you can see when you pull them. There is a small bleed orifice in there that you can't see, but if this gets plugged, it restricts both the flow to activate and the bleed-off to let it center.
Also check to make sure your aux spool is sliding freely in the valve body, and the condition of the centering springs.
Good Luck