Vision-language models (VLMs) like CLIP have been adapted for Multi-Label Recognition (MLR) with partial annotations by leveraging prompt-learning, where positive and negative prompts are learned for each class to associate their embeddings with class presence or absence in the shared vision-text feature space. While this approach improves MLR performance by relying on VLM priors, we hypothesize that learning negative prompts may be suboptimal, as the datasets used to train VLMs lack image-caption pairs explicitly focusing on class absence. To analyze the impact of positive and negative prompt learning on MLR, we introduce PositiveCoOp and NegativeCoOp, where only one prompt is learned with VLM guidance while the other is replaced by an embedding vector learned directly in the shared feature space without relying on the text encoder. Through empirical analysis, we observe that negative prompts degrade MLR performance, and learning only positive prompts, combined with learned negative embeddings (PositiveCoOp), outperforms dual prompt learning approaches. Moreover, we quantify the performance benefits that prompt-learning offers over a simple vision-features-only baseline, observing that the baseline displays strong performance comparable to dual prompt learning approach (DualCoOp), when the proportion of missing labels is low, while requiring half the training compute and 16 times fewer parameters