I found an old picture. My chute lever is now on the right side so my left hand never has to come off the wheel. You can see my cables pass thru my cage uprights. In the cage, steel brake tubing is welded in. This way they aren't on the inside getting hung up on my suit, and they aren't outside, subject to interference.
Both of my chutes are on one lever, both come out every pass. Overkill big time (180mph car) but a) it makes great pics, b) i like it c) i have a backup chute.
Some people claim this isn't NHRA legal, it's been tagged, many times, by the best and they have no issues with it.