Many patients with diabetes struggle with post-meal high blood glucose due to missed or untimely meal-related insulin doses. To address this challenge, our research aims to: (1) study mealtime patterns in patients with type 1 diabetes using wearable insulin pump data, and (2) develop personalized models for predicting future mealtimes to support timely insulin dose administration. Using two independent datasets with over 45,000 meal logs from 82 patients with diabetes, we find that the majority of people ( 60%) have irregular and inconsistent mealtime patterns that change notably through the course of each day and across months in their own historical data. We also show the feasibility of predicting future mealtimes with personalized LSTM-based models that achieve an average F1 score of > 95% with less than 0.25 false positives per day. Our research lays the groundwork for developing a meal prediction system that can nudge patients with diabetes to administer bolus insulin doses before meal consumption to reduce the occurrence of post-meal high blood glucose.