Unsupervised learning of node embeddings for directed graphs (digraphs) requires careful handling to ensure unbiased modelling. This paper addresses two key challenges: (1) the obstruction of information propagation in random walk and message-passing methods due to local sinks, and (2) the representation of multiple multi-step directed neighbourhoods, arising from the distinction between in-and out-neighbours. These challenges are interconnected—local sinks can be mitigated by treating the graph as undirected, but this comes at the cost of discarding all directional information. We make two main contributions to unsupervised embedding learning for digraphs. First, we introduce ReachNEs (Reachability Node Embeddings), a general framework for analysing embedding models and diagnosing local sink behaviour on digraphs. ReachNEs defines the reachability filter, a matrix polynomial over normalized adjacency matrices that captures multi-step, direction-sensitive proximity. It unifies the analysis of message-passing and random walk models, making its insights applicable across a wide range of embedding methods. Second, we propose DirSwitch, a novel embedding model that resolves both local sink bias and neighbourhood multiplicity via switching random walks. These walks use directed edges for local steps, preserving directional structure, then switch to undirected edges for long-range transitions, enabling escape from local sinks and improving information dispersal. Empirical results on node classification benchmarks demonstrate that DirSwitch consistently outperforms state-of-the-art unsupervised digraph proximity embedding methods, and also serves as a flexible digraph extension for self-supervised graph neural networks.