In order for the gyroscopic effect to be elicited motion is required. When the rotation rate of the outer gimbal goes back to zero the gyroscopic response to it ceases.
Later edit:
In writing the above paragraph I failed to take into account that it is specified that the question is for the case of absence of any friction.
In the absence of any friction:
When the force on the outer gimbal ceases to be exerted the motion of the gyro wheel transitions to nutation only. (This motion pattern is also referred to as 'torque free precession', which is a confusing name, because the motion pattern of nutation is distinct from the motion pattern of gyroscopic precession.)
In the absence of any friction the motion pattern of nutation will continue forever.
(Actually, the motion pattern of nutation gives rise to internal stresses in the gyro wheel. These internals stresses lead to flexing of the material. This flexing is very small of course, but it is non-zero. Over time this flexing will dissipate kinetic energy. To eliminate this dissipation altogether the gyro wheel would have to consist of an infinitely rigid material. )
Later later edit:
The onset of gyroscopic precession is actually the onset of a linear combination of two motions: gyroscopic precession and nutation. When the spin rate is high the rate of the nutation is high, and the amplitude of the nutation is small. With friction present the kinetic energy of the nutation is dissipated rapidly. Because of the rapid dissipation: usually the nutation is either not noticed at all, or if noticed dismissed as a transient thing.
In the case of frictionless motion:
It is possible to obtain an onset of gyroscipic precession while avoiding nutation, but it requires meticulous cancelation. In the absence of such meticulous cancelation: any change of applied torque gives onset of nutation (or if there is already nutation: change of state of nutation.) So: if you have steady gyroscopic precession, and no nutation: the force suddenly disappearing constitutes a change of the amount of force, and nutation will commence.
See also:
Tabletop experiment by Svilen Kostov and Daniel Hammer:
In that experiment: demonstration that onset of gyroscopic precession and onset of nutation are intrinsically linked:
'It has to go down a little in order to go around'
To understand the nature of the gyroscopic effect: there is a 2012 discussion by me of gyroscopic precession
The explanation there capitalizes on symmetry. (The concept of vector angular momentum is not used.)
