My tangle pattern: Vorago
When you look at Vorago, it should seem familiar, if you've played with my interlace patterns. It's sort of the scaffolding of a basic design for building that kind of pattern. As you can see from the variations and my example, you can build on it in many ways. Leave it sparse--show off the bare bones--or slap on some eye-bending stripes or hatching. Use a grid and match them up. Draw one very large Vorago, and use it as a string.
You've got two ways to approach this.
You can create a very elegant, and brilliant interlace intersection with precise lines. I recommend a ruler and a solid flat surface. Going for elegance helps you learn to master your lines and make them do what you want.
Or think in interesting ways. I'm not saying this is better. It is both easier and harder.
Precision is an element of interest, in and of itself. But if you forgo precision, you must replace it with other elements of interest. Dramatic shading, that can both enhance and hide unintended curves or unmatched lines. If you don't want to attempt pristine straight lines, plan on curves or wiggles. If your lines don't match, fill in with rough hatching to indicate an uneven surface, or breakage. Surprise yourself, and take note of what worked for you and what didn't. Going for surprise helps you draw on creativity you might not use otherwise.
The main thing is to decide which way you want to go, and use the tools you need to achieve it.
Win-win, either way.