Yes, you do need support at the end of the tube where it goes through the firewall. Some of the aftermarket suppliers make a bracket kit for this issue. You can make one with an angle bracket and a clamp which is pretty much what they are going to sell you. It can be covered up by the mat or carpet.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine