Efficient matching in ride-hailing and ride-pooling services depends not only on how matches are constructed, but also on when the platform triggers a matching operation. Many systems use batched matching with a fixed time interval to accumulate requests before matching, which increases the candidate set but cannot adapt to real time supply-demand fluctuations and may induce unnecessary waiting. This paper proposes a reinforcement learning approach that learns when to trigger matching based on current system conditions. We formulate the timing problem as a finite-horizon Markov decision process and train the policy using the Proximal Policy Optimization algorithm. To address sparse and delayed feedback, we introduce a finite-horizon, potential-based reward shaping scheme that preserves the optimal policy while densifying the learning signal; the same framework applies to both ride-hailing and ride-pooling, where detour delay is incorporated into the reward for pooling. Using a data-driven simulator calibrated on NYC trip records, the learned policy adapts matching timing decisions to the current state of waiting requests and available drivers and outperforms fixed-interval, rule-based dynamic, and first-dispatch baselines. It reduces total waiting time by 3.1% in ride-hailing and 20.1% in ride-pooling, and detour delay by 36.1% in pooling, while maintaining short matching times. ... Read more