Hey Grayson! Welcome to SoCalHiker!
I’m not sure what “loop” you’re referring to up Mt San Jacinto. Most of the routes are an out-and-back. One of my favorite overnight options is taking the Palm Springs Aerial Tram up, then hiking to Round Valley to camp for the night. On the second day, wake up and summit San J and head back down.
Here’s my detailed guide to that route: https://socalhiker.net//hiking-mt-san-jacinto-via-the-palm-springs-aerial-tram/
When you read that, you’ll see a link to the permit application down near the bottom of the guide.
Note that wilderness permits are also required for day hikes up San Jacinto, but they are free and don’t need to be reserved in advance. For day hikes, you can stop at the ranger station in Long Valley and fill out a permit. It’s super easy.