Webhook plugin & hooking into Contact Form
I had a similar issue where some queues would only run when I logged in via the control panel. The root cause is usually stalled or failed tasks, but I was able to get webhook tasks to run instantly by installing the AsyncQueue plugin.

From their docs:


  This plugin replaces Craft's default queue handler and moves queue execution to a non-blocking background process. The command craft queue/run gets executed right after you push a Job to the queue.