Let's try to isolate the source, the sound appear under the following conditions:-
- after warmed up
- when moving low speed ~10~20mph
- on both diesel (jtdm) and petrol (JTS) engine cars
- manual gearbox
- when accelerating (load), no sound when throttle is lifted or on free gear rolling
Hence, it is unlikely to be caused by:-
- fuel pump, unlikely both diesel and petrol generate same sound
- power steering pump, otherwise there will be sound when car not moving with engine running
I think the source is from part/parts where jtdm and jts has in common, such as gearbox, clutch, flywheel and drive shaft.
I am suggesting the dual mass flywheel because it could be due to the spring and damping mechanism of the dual mass transiting from one state to the other at lower rev accelerating. At higher speed the damping state is constant hence sound is gone.
The sound appears only after warmed up because the flywheel mechanism expanded and come in tight contact.
What do you think?