Gears play an important role in transmission systems, allowing for high performance in terms of load capacity and efficiency. Common gear faults such as cracked teeth and pitted teeth, can occur as a result of contact fatigue, excessive load, or sudden impact. Starting from an initial stage, their steady growth can lead to irreparable damage and unexpected breakdowns that result in economic losses. Therefore, local tooth damage diagnosis of gears using advanced monitoring techniques is extremely important for the normal operation of drivelines and transmissions. The presence of local tooth damage produces transient impact in the vibration signals, which exhibit non-stationary and non-linear characteristics. Taking into account its ability to characterize the phase coupling between signal components caused by non-linearity, wavelet-based high order spectrum is considered to be effective to attain reliable fault-related features. Among others, wavelet bicoherence technology has been successfully applied to detect the artificially created gear faults under steady speed and load. However, in case the operating condition changes, the effectiveness of this method in detecting gear faults is still unclear. Additionally, the selection of the informative bi-frequency bands and the extraction of instantaneous diagnostic features is still a challenge. This may constraint the widespread application of wavelet-based high order spectrum in gear fault diagnosis. This paper presents a novel strategy for selecting informative bi-frequency bands and extracting instantaneous diagnostic features in the time bi-frequency domain. The performance of the proposed methodology is evaluated by comparison with the WIF method and is extended to cases involving healthy and faulty gears operating under different speeds and loads. To validate the effectiveness of the methodology, an experimental dataset with artificially made gear pitting damage and a publicly available dataset which includes gears with various crack severity as well as different speed and load operating conditions is utilized.