Visual Prompt Tuning (VPT) is an effective tuning method for adapting pretrained Vision Transformers (ViTs) to downstream tasks. It leverages extra learnable tokens, known as prompts, which steer the frozen pretrained ViTs. Although VPT has demonstrated its applicability with supervised vision transformers, it often underperforms with self-supervised ones. Through empirical observations, we deduce that the effectiveness of VPT hinges largely on the ViT blocks with which the prompt tokens interact. Specifically, VPT shows improved performance on image classification tasks for MAE and MoCo v3 when the prompt tokens are inserted into later blocks rather than the first block. These observations suggest that there exists an optimal location of blocks for the insertion of prompt tokens. Unfortunately, identifying the optimal blocks for prompts within each self-supervised ViT for diverse future scenarios is a costly process. To mitigate this problem, we propose a simple yet effective method that learns a gate for each ViT block to adjust its intervention into the prompt tokens. With our method, prompt tokens are selectively influenced by blocks that require steering for task adaptation. Our method outperforms VPT variants in FGVC and VTAB image classification and ADE20K semantic segmentation. The code is available at https://github.com/ryongithub/GatedPromptTuning.