The question is
Is there a gyro effect on a jet engine such as the prop engine
If so what is this effect in terms of vector force compare to thrust force?
Need to be careful in comparing a vector with a force, they are not the same.
But the gyro direction is perpindicular to the long axis of the fan/prop shaft. It also follows the right hand rule which is 90 degree out of phase with any lateral motion of the fan shaft. It does not respond to fore or aft motion of the shaft (thrust), however it does generate force in response to RPM, but not torque, but only in combination with a lateral motion of its shaft.
OK, so if the fan/prop shaft is held on its bearings, and the bearings are held rigidly within the engine cases, which are held firmly on the pylon mounts and you don't horse the aircraft arround enough to break off its tail or wings, then the gyro forces are quite minimal and almost never show up in literature having to do with commercial aviation.
Comparatively speaking the gyro forces are very minor with the small diameter engines but very significant on the large diameter fans should you happen to break off an engine while its running at very high power and allow it to take its own pitch or yaw attitude free of the wing.
On the other hand failed engines run down (sometimes abruptly0, and while generating torque, they do not generate significant gyro loads.