Hello. I faced a similar problem during my normal playthrough. The spider cavern did not spawn anywhere in the spider forest. However, I found it on the flayer jungle. On that map, there was a small branch with the spider cavern entrance. It was curious because that branch was not connected to the spider forest however, it was considered as part of the spider forest.
When you first enter, go either upright or downleft to find the first bridge. From here, you will be in the 2x2 area, where you want to check all the upleft and downright exits. This is the slowest part of the cavern, but by skipping known dead ends you can still significantly cut your time off here. Once you find the windy path, you'll know you're in the right place. As soon as you cross that path, the exit is always upright from that area.