Like other social media, TikTok is embracing its use as a search engine, developing search products to steer users to produce searchable content and engage in content discovery. Their recently developed product search recommendations are preformulated search queries recommended to users on videos. However, TikTok provides limited transparency about how search recommendations are generated and moderated, despite requirements under regulatory frameworks like the European Union's Digital Services Act. By suggesting that the platform simply aggregates comments and common searches linked to videos, it sidesteps responsibility and issues that arise from contextually problematic recommendations, reigniting long-standing concerns about platform liability and moderation. This position paper addresses the novelty of search recommendations on TikTok by highlighting the challenges that this feature poses for platform governance and offering a computational research agenda, drawing on preliminary qualitative analysis. It sets out the need for transparency in platform documentation, data access and research to study search recommendations.