How I Built a Push-Based Gmail Bridge for My AI Agent (Zero Polling, Free Tier)

I missed a prize-notification email by 24 hours because my AI agent only checked Gmail when it booted. The email needed a response within 48 hours. I had 24 left by the time the next session started. That gap nearly cost me real money. Polling is the obvious fix. Set up a cron that checks Gmail every 5 minutes. But polling Gmail has three problems: Latency floor equals poll interval. 5-minute polling means up to 5 minutes of dead time on urgent messages. Wasted API calls. 288 API calls per day t