This is a video from me, DarkspinesSonic A.K.A Da1AndOnlySonic, showing how to get the ancient light upgrade (light speed attack) immediately after finishing Emerald Coast. (Will probably add annotations later)

Several things to note, to run up the wall as seen near the beginning of the video, all you have to do is spindash towards the wall while on top of the rock. You'll notice the rock has certain slants on it, and by spindashing off the slants at full speed, it'll allow you to run on the wall. While on the rock, you can spindash on parts that have a very noticeable slant on them, one of those slants are seen in the video (the slant that I spindash on). I highly recommend you switch the camera to free mode for this part as I do in the video.

Once you make it into the tunnel, you'll notice I have a light speed dash ready, and still spindash. For that, all you have to do is use B or X for the initial charge, then while holding onto whichever button you chose, use the other button you didn't use to start a spindash. You can let go of your spindash and Sonic won't use his light speed dash until he stops rolling, so you can cancel your roll by holding B or X and still keep your light dash ready as seen in the video.

As for the running on the ceiling deal, I'll do my best to explain how it's done. After you spindash to get some speed, be sure to hold forward on the analog stick. This will have you running on the ceiling of the tunnel. Controlling where you will run after this part is a simple concept to follow. The more you move your analog stick clockwise, the more to the left Sonic will go on-screen, and vice versa if you move your analog stick counter-clockwise. Your objective is to hit the top left corner of the door blocking the exit to the cave, while having enough speed to go through it. As you go further down the cave, Sonic begins to move towards the right of the cave. If he goes over too much to the right, he will fall down. Basically, you have to move the analog stick clockwise as you go further down the cave. Use the video as a reference to see how Sonic should be going down the cave, you'll get it soon enough. From my personal experience, I end up having the analog stick at down-right by the time I reach the top left corner of the door. Although I have gone through before and not needed the light speed dash, it will more than likely be necessary to use. All you have to do after successfully going through the cave wall/door is hold left on the analog stick and release B/X to do the light speed dash as seen in the video (I decided to leave in the failed attempt just for the lol).

You can now go and get the upgrade. The door is solid on both sides unfortunately, but no matter, all you have to do is quit the game after getting the upgrade and then go back to Sonic's story. That's all there is to know in regards to getting the ancient light upgrade. After getting the upgrade, I decided to go to Red Mountain. To see what happens, just watch the video (all I will say about it is no escape...for now anyway). Enjoy!^_^ (less info)