what is the order of your reverse current? What is the shape of these fluctuations? The instability of the transistor is observed when you have continuous change of the current with time. Bit if you have fluctuations then can can be caused by noise and interference from other near by sources.
If you display your curves, one can give more precise comment.
It may (depending on the size of the measured current) simply be noise in the system or a sign that one or more electrical connections are unstable. I would suggest checking that all the wires/leads are securely physically connected and maybe changing some of them (e.g. use a different lead from the power supply to the device), and seeing if this has any effect on the leakage current.
Leak currents are usually time independent, continuous or stable at a given voltage range that they are active. But leak currents do not make sudden fluctuations-jitters or zigzags as you mentioned. I agree with previous comments that it is either due to noise or blockage of the electrode tip inable to pass current.
Tell us how do you connect your transistor while measuring the blue and the red curves. I think while measuring the blue line you left one of the electrodes of the transistor open. So, to resolve this issue you do not leave any electrode floating or open circuit. This my expectation.
If I comment your IV characteristic, your Igs is bit higher (1E9), noticed that your Ion is 1E5. May be your insulator layer had a lot of defect (bad insolator) or your SCO .
the favorable value of Igs is the lowest is possible. in the figure, your Igs is 1E-9 A. it is better if the Igs is lower, in this case, than 1E-11 for example.
if it possible, you have to perform more characteristics (like Positive/negative biass stress) in order to quatify the performance of your OTFT and also to understand the mechanism of instability in your OTFT (maybe caused by the insolator or the degradation of you OSC under stress).