Learning transferable representations for electroencephalography (EEG) remains challenging because EEG signals are inherently multi-channel and non-stationary. Channels observed at the same time provide coupled measurements of neural activity, while the relevant temporal dynamics vary across contexts. This structure is poorly matched by architectures that apply uniform computation across time or route each channel patch independently. To this end, we propose TRACE, an autoregressive EEG pre-training framework that predicts future EEG patches from causal context while performing temporally adaptive and cross-channel coherent computation. At each temporal step, TRACE derives an expert routing decision from the causal cross-channel history and applies it jointly to all channels at that step. This preserves instantaneous cross-channel coherence while allowing different temporal regimes to activate different computation. Since routing is defined over the available channel set and causal temporal context, TRACE is compatible with heterogeneous pre-training across corpora with different channel counts, montages, sequence lengths, and recording domains. Across eight downstream EEG benchmarks, TRACE is evaluated in both settings: when downstream domains are seen only as unlabeled pre-training data and when downstream datasets are completely unseen during pre-training. It obtains the best results on several benchmarks while remaining competitive on motor imagery and clinical event classification tasks, with ablations supporting the importance of cross-channel temporal routing.